Forward Purchase Agreement, dated February 26, 2021, by and between the Company and HEC Master Fund LP

Exhibit 10.6

FORWARD PURCHASE AGREEMENT

This Forward Purchase Agreement (this “Agreement”) is entered into as of February 26, 2021, by and between Hudson Executive Investment Corp. III, a Delaware corporation (the “Company”), and HEC Master Fund LP, a Delaware limited partnership (the “Purchaser”).

Recitals

WHEREAS, the Company was incorporated for the purpose of effecting a merger, capital stock exchange, asset acquisition, stock purchase, reorganization or similar business combination with one or more businesses (a “Business Combination”);

WHEREAS, the Company has filed with the U.S. Securities and Exchange Commission (the “SEC”) a registration statement on Form S-1, as amended (the “Registration Statement”), for its initial public offering (“IPO”) of 52,500,000 units (or 60,375,000 units if the underwriters’ over-allotment option (the “IPO Option”) is exercised in full) (the “Public Units”) at a price of $10.00 per Public Unit, each Public Unit comprised of one share of the Company’s Class A common stock, par value $0.0001 per share (the “Class A Shares,” and the Class A Shares included in the Public Units, the “Public Shares”), and one-fifth of one redeemable warrant, where each whole redeemable warrant is exercisable to purchase one Class A Share at an exercise price of $11.50 per share (the “Warrants,” and the Warrants included in the Public Units, the “Public Warrants”);

WHEREAS, the Company’s sponsor, HEC Sponsor III LLC, has agreed to purchase an aggregate of 8,333,333 warrants (or 9,383,333 warrants if the IPO Option is exercised in full) at a price of $1.50 per warrant in a private placement that will close simultaneously with the closing of the IPO (the “Private Placement Warrants”);

WHEREAS, following the closing of the IPO (the “IPO Closing”), the Company will seek to identify and consummate a Business Combination;

WHEREAS, the parties wish to enter into this Agreement, pursuant to which, concurrently with the closing of the Company’s initial Business Combination (the “Business Combination Closing”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, on a private placement basis, the number of units (the “Forward Purchase Units”) determined pursuant to Sections 1(a)(ii), (iii) and (iv) hereof, each comprised of one Class A Share (each, a “Forward Purchase Share”) and one-fifth of one warrant (each, a “Forward Purchase Warrant”), on the terms and conditions set forth herein (the Forward Purchase Shares, the Forward Purchase Warrants underlying the Forward Purchase Units and the Class A Shares underlying the Forward Purchase Warrants, the “Forward Purchase Securities”);

WHEREAS, proceeds from the IPO and the sale of the Private Placement Warrants in an aggregate amount equal to the gross proceeds from the IPO will be deposited into a trust account for the benefit of the holders of the Public Shares (the “Trust Account”), as described in the Registration Statement; and

WHEREAS, the amounts available to the Company from the Trust Account (after giving effect to any redemptions of Public Shares) and any other equity or debt financing obtained by the Company in connection with the Business Combination (the “Available Cash”), together with the proceeds from the sale of the Forward Purchase Units, will be used to satisfy the cash requirements of the Business Combination, including funding the purchase price and paying expenses and retaining amounts specified in the definitive agreement for the Business Combination (the “Definitive Agreement”) to be retained for use by the post-Business Combination company for working capital or other purposes (the “Cash Requirements”);

NOW, THEREFORE, in consideration of the premises, representations, warranties and the mutual covenants contained in this Agreement, and for other good and valuable consideration, the receipt, sufficiency and adequacy of which are hereby acknowledged, the parties hereto agree as follows:

Agreement

1. Sale and Purchase.

(a) Forward Purchase Units.

(i) Subject to Sections 1(a)(ii), (iii) and (iv), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to a maximum of 5,000,000 Forward Purchase Units (the “Maximum Units”) for a purchase price of $10.00 per Forward Purchase Unit (the “Forward Purchase Price”), or up to a maximum of $50,000,000 in the aggregate. Each Forward Purchase Warrant will have the same terms as each Private Placement Warrant, and will be subject to the terms and conditions of the Warrant Agreement to be entered into between the Company and Continental Stock Transfer & Trust Company, as Warrant Agent, in connection with the IPO, mutatis mutandis.

(ii) The number of Forward Purchase Units to be issued and sold by the Company and purchased by the Purchaser hereunder shall be determined as follows:

(A) As soon as reasonably practicable, but in no event less than ten (10) Business Days prior to the Company’s entry into the Definitive Agreement, the Company shall provide the Purchaser with notice (the “Initial Company Notice”) of the number of Forward Purchase Units that it desires the Purchaser to purchase pursuant to this Agreement, which shall be equal to its good faith estimate of that number which, after payment of the aggregate Forward Purchase Price by the Purchaser, will result in gross proceeds to the Company equal to the amount of funds necessary for the Company to satisfy the Cash Requirements less the Available Cash; provided, however, that such number shall in no event exceed the Maximum Units; and provided, further, that, notwithstanding the foregoing, the Purchaser shall in any event have the option to purchase up to the Maximum Units. Following delivery of the Initial Company Notice, the Company shall provide the Purchaser with such other information as the Purchaser (or any applicable Transferee pursuant to Section 4(b) hereof) may reasonably request so that the Purchaser (or such Transferee) may seek the approval of its investment committee to consummate the purchase of the Forward Purchase Units hereunder.

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(B) Within five (5) Business Days after receipt of the Initial Company Notice, the Purchaser shall provide the Company with notice (the “Initial Purchaser Notice”) of the decision of its investment committee as to the number of Forward Purchase Units it wishes to purchase pursuant to this Agreement, if any, which shall not exceed the Maximum Units, which notice shall constitute the binding obligation of the Purchaser to purchase such number of Forward Purchase Units, subject to the terms and conditions of this Agreement.

(iii) At least two (2) Business Days before the Business Combination Closing, the Company shall provide the Purchaser with an updated notice (the “Final Company Notice”) including:

(A) its determination, based on the actual number of Public Shares validly submitted for redemption or other changes in the Cash Requirements, of the number of Forward Purchase Units that it desires the Purchaser to purchase pursuant to this Agreement;

(B) the anticipated date of the Business Combination Closing; and

(C) instructions for wiring the Forward Purchase Price.

(iv) At least one (1) Business Day before the Business Combination Closing, the Purchaser shall provide the Company with an updated notice (the “Final Purchaser Notice”) of the number of Forward Purchase Units it will be obligated to purchase pursuant to this Agreement, with no further notification or confirmation necessary from the Company, which number shall not be less than the lesser of (A) the number of Forward Purchase Units that the Purchaser was obligated to purchase pursuant to Section 1(a)(ii) as indicated in the Initial Purchaser Notice and (B) the number of Forward Purchase Units that the Company desires the Purchaser to purchase as specified in the Final Company Notice.

(v) The closing of the sale of Forward Purchase Units (the “Forward Closing”) shall be held on the same date and concurrently with the Business Combination Closing (such date being referred to as the “Forward Closing Date”). At least one (1) Business Day prior to the Forward Closing Date, the Purchaser shall deliver to the Company the Forward Purchase Price for the Forward Purchase Units by wire transfer of U.S. dollars in immediately available funds to the account specified by the Company in such notice to be held in escrow until the Forward Closing. Immediately prior to the Forward Closing on the Forward Closing Date, (i) the Forward Purchase Price shall be released from escrow automatically and without further action by the Company or the Purchaser, and (ii) upon such release, the Company shall issue the Forward Purchase Units to the Purchaser in book-entry form, free and clear of any liens or other restrictions whatsoever (other than those arising under state or federal securities laws), registered in the name of the Purchaser (or its nominee in accordance with its delivery instructions), or to a custodian designated by the Purchaser, as applicable. In the event the Business Combination Closing does not occur within five (5) Business Days of the date scheduled for closing, the Forward Closing shall not occur and the Company shall promptly (but not later than one (1 Business Day thereafter) return the Forward Purchase Price to the Purchaser. For purposes of this Agreement, “Business Day” means any day, other than a Saturday or a Sunday, that is neither a legal holiday nor a day on which banking institutions are generally authorized or required by law or regulation to close or be closed in the City of New York, New York; provided, however, for clarification, commercial banks in the City of New York shall not be

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deemed to be authorized or required by law or regulation to close or be closed due to “stay at home”, “shelter-in-place”, “non-essential employee” or any other similar orders or restrictions or the closure of any physical branch locations at the direction of any governmental authority so long as the electronic funds transfer systems (including for wire transfers) of commercial banks in the City of New York are open for use by customers on such day.

(b) Legends. Each register and book entry for the Forward Purchase Securities shall contain a notation, and each certificate (if any) evidencing the Forward Purchase Securities shall be stamped or otherwise imprinted with a legend, in substantially the following form:

“THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY STATE OR OTHER JURISDICTION, AND MAY NOT BE TRANSFERRED IN VIOLATION OF SUCH ACT AND LAWS. THE SALE, PLEDGE, HYPOTHECATION, OR TRANSFER OF THE SECURITIES REPRESENTED HEREBY ARE SUBJECT TO THE TERMS AND CONDITIONS OF A CERTAIN FORWARD PURCHASE AGREEMENT BY AND BETWEEN THE HOLDER AND THE COMPANY. COPIES OF SUCH AGREEMENT MAY BE OBTAINED UPON WRITTEN REQUEST TO THE SECRETARY OF THE COMPANY.”

2. Representations and Warranties of the Purchaser. The Purchaser represents and warrants to the Company as follows, as of the date hereof:

(a) Organization and Power. The Purchaser is duly organized, validly existing, and in good standing under the laws of the jurisdiction of its formation and has all requisite power and authority to carry on its business as presently conducted and as proposed to be conducted.

(b) Authorization. The Purchaser has full power and authority to enter into this Agreement. This Agreement, when executed and delivered by the Purchaser, will constitute the valid and legally binding obligation of the Purchaser, enforceable against the Purchaser in accordance with its terms, except (i) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance and any other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies, or (iii) to the extent the indemnification provisions contained in the Registration Rights (as defined below) may be limited by applicable federal or state securities laws.

(c) Governmental Consents and Filings. No consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state or local governmental authority is required on the part of the Purchaser in connection with the consummation of the transactions contemplated by this Agreement.

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(d) Compliance with Other Instruments. The execution, delivery and performance by the Purchaser of this Agreement and the consummation by the Purchaser of the transactions contemplated by this Agreement will not result in any violation or default (i) of any provisions of its organizational documents, (ii) of any instrument, judgment, order, writ or decree to which it is a party or by which it is bound, (iii) under any note, indenture or mortgage to which it is a party or by which it is bound, (iv) under any lease, agreement, contract or purchase order to which it is a party or by which it is bound or (v) of any provision of federal or state statute, rule or regulation applicable to the Purchaser, in each case (other than clause (i)),which would have a material adverse effect on the Purchaser or its ability to consummate the transactions contemplated by this Agreement.

(e) Purchase Entirely for Own Account. This Agreement is made with the Purchaser in reliance upon the Purchaser’s representation to the Company, which by the Purchaser’s execution of this Agreement, the Purchaser hereby confirms, that the Forward Purchase Securities to be acquired by the Purchaser will be acquired for investment for the Purchaser’s own account, not as a nominee or agent, and not with a view to the resale or distribution of any part thereof in violation of any state or federal securities laws, and that the Purchaser has no present intention of selling, granting any participation in, or otherwise distributing the same in violation of law. By executing this Agreement, the Purchaser further represents that the Purchaser does not presently have any contract, undertaking, agreement or arrangement with any Person to sell, transfer or grant participations to such Person or to any third Person, with respect to any of the Forward Purchase Securities. For purposes of this Agreement, “Person” means an individual, a limited liability company, a partnership, a joint venture, a corporation, a trust, an unincorporated organization, any other entity or any government or any department or agency thereof.

(f) Disclosure of Information. The Purchaser has had an opportunity to discuss the Company’s business, management, financial affairs and the terms and conditions of the offering of the Forward Purchase Units, as well as the terms of the Company’s proposed IPO, with the Company’s management.

(g) Restricted Securities. The Purchaser understands that the offer and sale of the Forward Purchase Units to the Purchaser has not been, and will not be, registered under the Securities Act of 1933, as amended (the “Securities Act”), by reason of a specific exemption from the registration provisions of the Securities Act which depends upon, among other things, the bona fide nature of the investment intent and the accuracy of the Purchaser’s representations as expressed herein. The Purchaser understands that the Forward Purchase Securities are “restricted securities” under applicable U.S. federal and state securities laws and that, pursuant to these laws, the Purchaser must hold the Forward Purchase Securities indefinitely unless they are registered with the SEC and qualified by state authorities, or an exemption from such registration and qualification requirements is available. The Purchaser acknowledges that the Company has no obligation to register or qualify the Forward Purchase Securities, or any Class A Shares into which the Forward Purchase Securities may be converted or exercised, for resale, except for the Registration Rights. The Purchaser further acknowledges that if an exemption from registration or qualification is available, it may be conditioned on various requirements including, but not limited to, the time and manner of sale, the holding period for the Forward Purchase Securities, and on requirements relating to the Company which are outside of the Purchaser’s control, and which the Company is under no obligation and may not be able to satisfy. The Purchaser acknowledges that the Company filed the Registration Statement for its proposed IPO. The Purchaser understands that the offering of the Forward Purchase Securities is not, and is not intended to be, part of the IPO, and that the Purchaser will not be able to rely on the protection of Section 11 of the Securities Act with respect to the Forward Purchase Securities.

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(h) No Public Market. The Purchaser understands that no public market now exists for the Forward Purchase Securities, and that the Company has made no assurances that a public market will ever exist for the Forward Purchase Securities.

(i) High Degree of Risk. The Purchaser understands that its agreement to purchase the Forward Purchase Securities involves a high degree of risk which could cause the Purchaser to lose all or part of its investment.

(j) Accredited Investor. The Purchaser is an accredited investor as defined in Rule 501(a) of Regulation D promulgated under the Securities Act.

(k) No General Solicitation. Neither the Purchaser, nor any of its officers, directors, employees, agents, stockholders or partners has either directly or indirectly, including, through a broker or finder (i) engaged in any general solicitation, or (ii) published any advertisement in connection with the offer and sale of the Forward Purchase Units.

(l) Residence. The Purchaser’s principal place of business is the office or offices located at the address of the Purchaser set forth on the signature page hereof.

(m) Non-Public Information. The Purchaser acknowledges its obligations under applicable securities laws with respect to the treatment of non-public information relating to the Company.

(n) Adequacy of Financing. At the time of the Forward Closing, the Purchaser will have available to it sufficient funds to satisfy its obligations under this Agreement.

(o) No Other Representations and Warranties; Non-Reliance. Except for the specific representations and warranties contained in this Section 2 and in any certificate or agreement delivered pursuant hereto, none of the Purchaser nor any person acting on behalf of the Purchaser nor any of the Purchaser’s affiliates (the “Purchaser Parties”) has made, makes or shall be deemed to make any other express or implied representation or warranty with respect to the Purchaser and this offering, and the Purchaser Parties disclaim any such representation or warranty. Except for the specific representations and warranties expressly made by the Company in Section 3 of this Agreement and in any certificate or agreement delivered pursuant hereto, the Purchaser Parties specifically disclaim that they are relying upon any other representations or warranties that may have been made by the Company, any person on behalf of the Company or any of the Company’s affiliates (collectively, the “Company Parties”).

3. Representations and Warranties of the Company. The Company represents and warrants to the Purchaser as follows:

(a) Incorporation and Corporate Power. The Company is a corporation duly incorporated and validly existing and in good standing as a corporation under the laws of the State of Delaware and has all requisite corporate power and authority to carry on its business as presently conducted and as proposed to be conducted. The Company has no subsidiaries.

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(b) Capitalization. On the date hereof, the authorized share capital of the Company consists of:

(i) 380,000,000 Class A Shares, none of which are issued and outstanding.

(ii) 20,000,000 shares of the Company’s Class B common stock, par value $0.0001 per shares (the “Class B Shares”), 15,093,750 of which are issued and outstanding. All of the outstanding Class B Shares have been duly authorized, are fully paid and nonassessable and were issued in compliance with all applicable federal and state securities laws.

(iii) 1,000,000 preferred shares, none of which are issued and outstanding.

(c) Authorization. All corporate action required to be taken by the Company’s Board of Directors and stockholders in order to authorize the Company to enter into this Agreement, and to issue the Forward Purchase Securities at the Forward Closing, and the securities issuable upon exercise of the Forward Purchase Warrants, has been taken or will be taken prior to the Forward Closing. All action on the part of the stockholders, directors and officers of the Company necessary for the execution and delivery of this Agreement, the performance of all obligations of the Company under this Agreement to be performed as of the Forward Closing, and the issuance and delivery of the Forward Purchase Securities and the securities issuable upon exercise of the Forward Purchase Warrants has been taken or will be taken prior to the Forward Closing. This Agreement, when executed and delivered by the Company, shall constitute the valid and legally binding obligation of the Company, enforceable against the Company in accordance with its terms except (i) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, or other laws of general application relating to or affecting the enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief, or other equitable remedies, or (iii) to the extent the indemnification provisions contained in the Registration Rights may be limited by applicable federal or state securities laws.

(d) Valid Issuance of Securities. The Forward Purchase Securities, when issued, sold and delivered in accordance with the terms and for the consideration set forth in this Agreement, and the securities issuable upon exercise of the Forward Purchase Warrants, when issued in accordance with the terms of the Forward Purchase Warrants and this Agreement, will be validly issued, fully paid and nonassessable, as applicable, and free of all preemptive or similar rights, taxes, liens, encumbrances and charges with respect to the issue thereof and restrictions on transfer other than restrictions on transfer specified under this Agreement, applicable state and federal securities laws and liens or encumbrances created by or imposed by the Purchaser. Assuming the accuracy of the representations of the Purchaser in this Agreement and subject to the filings described in Section 3(e) below, the Forward Purchase Securities will be issued in compliance with all applicable federal and state securities laws.

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(e) Governmental Consents and Filings. Assuming the accuracy of the representations and warranties made by the Purchaser in this Agreement, no consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state or local governmental authority is required on the part of the Company in connection with the consummation of the transactions contemplated by this Agreement, except for filings pursuant to Regulation D of the Securities Act, and applicable state securities laws, if any, and pursuant to the Registration Rights.

(f) Compliance with Other Instruments. The execution, delivery and performance of this Agreement and the consummation of the transactions contemplated by this Agreement will not result in any violation or default (i) of any provisions of the Company’s certificate of incorporation, as it may be amended from time to time (the “Charter”), bylaws or other governing documents of the Company, (ii) of any instrument, judgment, order, writ or decree to which the Company is a party or by which it is bound, (iii) under any note, indenture or mortgage to which the Company is a party or by which it is bound, (iv) under any lease, agreement, contract or purchase order to which the Company is a party or by which it is bound or (v) of any provision of federal or state statute, rule or regulation applicable to the Company, in each case (other than clause (i)) which would have a material adverse effect on the Company or its ability to consummate the transactions contemplated by this Agreement.

(g) Operations. As of the date hereof, the Company has not conducted, and prior to the IPO Closing the Company will not conduct, any operations other than organizational activities and activities in connection with offerings of its securities.

(h) No General Solicitation. Neither the Company, nor any of its officers, directors, employees, agents or stockholders has either directly or indirectly, including, through a broker or finder (i) engaged in any general solicitation, or (ii) published any advertisement in connection with the offer and sale of the Forward Purchase Units.

(i) No Other Representations and Warranties; Non-Reliance. Except for the specific representations and warranties contained in this Section 3 and in any certificate or agreement delivered pursuant hereto, none of the Company Parties has made, makes or shall be deemed to make any other express or implied representation or warranty with respect to the Company, this offering, the proposed IPO or a potential Business Combination, and the Company Parties disclaim any such representation or warranty. Except for the specific representations and warranties expressly made by the Purchaser in Section 2 of this Agreement and in any certificate or agreement delivered pursuant hereto, the Company Parties specifically disclaim that they are relying upon any other representations or warranties that may have been made by the Purchaser Parties.

4. Registration Rights; Transfer

(a) Registration Rights. The Purchaser shall be granted registration rights by the Company with respect to the Forward Purchase Securities pursuant to a registration rights agreement to be entered into with the Company, a form of which has been filed with the registration statement relating to the Company’s IPO (the “Registration Rights”).

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(b) Transfer. This Agreement and all of the Purchaser’s rights and obligations hereunder (including the Purchaser’s obligation to purchase the Forward Purchase Units) may be transferred or assigned, at any time and from time to time, in whole or in part, to one or more affiliates of the Purchaser (each such transferee, a “Transferee”). Upon any such assignment:

(i) the applicable Transferee shall execute a signature page to this Agreement, substantially in the form of the Purchaser’s signature page hereto (the “Joinder Agreement”), which shall reflect the number of Forward Purchase Units to be purchased by such Transferee (the “Transferee Securities”), and, upon such execution, such Transferee shall have all the same rights and obligations of the Purchaser hereunder with respect to the Transferee Securities, and references herein to the “Purchaser” shall be deemed to refer to and include any such Transferee with respect to such Transferee and to its Transferee Securities; provided, that any representations, warranties, covenants and agreements of the Purchaser and any such Transferee shall be several and not joint and shall be made as to the Purchaser or any such Transferee, as applicable, as to itself only; and

(ii) upon a Transferee’s execution and delivery of a Joinder Agreement, the number of Forward Purchase Units to be purchased by the Purchaser hereunder shall be reduced by the total number of Forward Purchase Units to be purchased by the applicable Transferee pursuant to the applicable Joinder Agreement, which reduction shall be evidenced by the Purchaser and the Company amending Schedule A to this Agreement to reflect each transfer and updating the “Number of Forward Purchase Units” and “Aggregate Purchase Price for Forward Purchase Units” on the Purchaser’s signature page hereto to reflect such reduced number of Forward Purchase Units, and the Purchaser shall be fully and unconditionally released from its obligation to purchase such Transferee Securities hereunder. For the avoidance of doubt, this Agreement need not be amended and restated in its entirety, but only Schedule A and the Purchaser’s signature page hereto need be so amended and updated and executed by each of the Purchaser and the Company upon the occurrence of any such transfer of Transferee Securities.

5. Additional Agreements, Acknowledgements and Waivers of the Purchaser.

(a) Lock-up; Transfer Restrictions. The Purchaser agrees that it shall not Transfer any Forward Purchase Units (or the Forward Purchase Shares and Forward Purchase Warrants, including the Class A Shares issued or issuable upon the exercise of any such Forward Purchase Warrants) until 30 days after the completion of the initial Business Combination. Notwithstanding the foregoing, Transfers of the Forward Purchase Units (and the underlying Class A Shares and Warrants, including the Class A Shares issued or issuable upon the exercise of any such warrants) are permitted (any such transferees, the “Permitted Transferees”): (A) to the Company’s officers or directors, any affiliates or family members of any of the Company’s officers or directors, any members of the Purchaser, or any affiliates of the Purchaser; (B) in the case of an individual, by gift to a member of the individual’s immediate family, to a trust, the beneficiary of which is a member of individual’s immediate family or an affiliate of such person, or to a charitable organization; (C) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual; (D) in the case of an individual, pursuant to a qualified domestic relations order; (E) by private sales or transfers made in connection with the consummation of a Business Combination at prices no greater than the price at which the

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securities were originally purchased; (F) in the event of the Company’s liquidation prior to the completion of a Business Combination; (G) in the event of the Company’s liquidation, merger, capital stock exchange, reorganization or other similar transaction which results in all of the Company’s stockholders having the right to exchange their Class A Shares for cash, securities or other property subsequent to the completion of a Business Combination; (H) as a distribution to limited partners, members or stockholders of the Purchaser; (I) to the Purchaser’s affiliates, to any investment fund or other entity controlled or managed by the Purchaser or any of its affiliates, or to any investment manager or investment advisor of the Purchaser or an affiliate of any such investment manager or investment advisor; (J) to a nominee or custodian of a person or entity to whom a disposition or transfer would be permissible under clauses (A) through (I) above; (K) to the Purchaser or any Transferee hereunder; (L) by virtue of the laws of the Purchaser’s jurisdiction of formation or its organizational documents upon dissolution of the Purchaser; and (M) pursuant to an order of a court or regulatory agency; provided, however, that in the case of clauses (A) through (E) and (H) through (L), these Permitted Transferees must enter into a written agreement agreeing to be bound by these transfer restrictions. “Transfer” shall mean the (x) sale or assignment of, offer to sell, contract or agreement to sell, hypothecation, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position (within the meaning of Section 16 of the Exchange Act, and the rules and regulations of the SEC promulgated thereunder) with respect to, any of the Forward Purchase Securities (excluding any pledges in the ordinary course of business for bona fide financing purposes or as part of prime brokerage arrangements), (y) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any of the Forward Purchase Securities, whether any such transaction is to be settled by delivery of such Forward Purchase Securities, in cash or otherwise, or (z) public announcement of any intention to effect any transaction specified in clause (x) or (y).

(b) Trust Account.

(i) The Purchaser hereby acknowledges that it is aware that the Company will establish the Trust Account for the benefit of its public stockholders upon the IPO Closing. The Purchaser, for itself and its affiliates, hereby agrees that it has no right, title, interest or claim of any kind in or to any monies held in the Trust Account, or any other asset of the Company as a result of any liquidation of the Company, except for redemption and liquidation rights, if any, the Purchaser may have in respect of any Public Shares held by it.

(ii) The Purchaser hereby agrees that it shall have no right of set-off or any right, title, interest or claim of any kind (“Claim”) to, or to any monies in, the Trust Account, and hereby irrevocably waives any Claim to, or to any monies in, the Trust Account that it may have now or in the future, except for redemption and liquidation rights, if any, the Purchaser may have in respect of any Public Shares held by it. In the event the Purchaser has any Claim against the Company under this Agreement, the Purchaser shall pursue such Claim solely against the Company and its assets outside the Trust Account and not against the property or any monies in the Trust Account, except for redemption and liquidation rights, if any, the Purchaser may have in respect of any Public Shares held by it.

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6. Nasdaq Listing. The Company will use commercially reasonable efforts to effect the listing of the Class A Shares and Public Warrants on The Nasdaq Capital Market (“Nasdaq”) (or another national securities exchange) at the time of the Business Combination Closing.

7. Forward Closing Conditions.

(a) The obligation of the Purchaser to purchase the Forward Purchase Units at the Forward Closing under this Agreement shall be subject to the fulfillment, at or prior to the Forward Closing of each of the following conditions, any of which, to the extent permitted by applicable laws, may be waived by the Purchaser:

(i) The Business Combination shall be consummated substantially concurrently with the purchase of the Forward Purchase Units;

(ii) The Purchaser and any applicable Transferee shall have obtained the approval of its respective investment committee to consummate the purchase of the Forward Purchase Units hereunder as contemplated by Section 1(a)(ii) hereof;

(iii) The Company shall have delivered to the Purchaser a certificate evidencing the Company’s good standing as a Delaware corporation;

(iv) The representations and warranties of the Company set forth in Section 3 of this Agreement shall have been true and correct as of the date hereof and shall be true and correct as of the Forward Closing Date, as applicable, with the same effect as though such representations and warranties had been made on and as of such date (other than any such representation or warranty that is made by its terms as of a specified date, which shall be true and correct as of such specified date), except where the failure to be so true and correct would not have a material adverse effect on the Company or its ability to consummate the transactions contemplated by this Agreement;

(v) The Company shall have performed, satisfied and complied in all material respects with the covenants, agreements and conditions required by this Agreement to be performed, satisfied or complied with by the Company at or prior to the Forward Closing; and

(vi) No order, writ, judgment, injunction, decree, determination, or award shall have been entered by or with any governmental, regulatory, or administrative authority or any court, tribunal, or judicial, or arbitral body, and no other legal restraint or prohibition shall be in effect, preventing the purchase by the Purchaser of the Forward Purchase Units.

(b) The obligation of the Company to sell the Forward Purchase Units at the Forward Closing under this Agreement shall be subject to the fulfillment, at or prior to the Forward Closing of each of the following conditions, any of which, to the extent permitted by applicable laws, may be waived by the Company:

(i) The Business Combination shall be consummated substantially concurrently with the purchase of Forward Purchase Units;

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(ii) The representations and warranties of the Purchaser set forth in Section 2 of this Agreement shall have been true and correct as of the date hereof and shall be true and correct as of the Forward Closing Date, as applicable, with the same effect as though such representations and warranties had been made on and as of such date (other than any such representation or warranty that is made by its terms as of a specified date, which shall be true and correct as of such specified date), except where the failure to be so true and correct would not have a material adverse effect on the Purchaser or its ability to consummate the transactions contemplated by this Agreement;

(iii) The Purchaser shall have performed, satisfied and complied in all material respects with the covenants, agreements and conditions required by this Agreement to be performed, satisfied or complied with by the Purchaser at or prior to the Forward Closing; and

(iv) No order, writ, judgment, injunction, decree, determination, or award shall have been entered by or with any governmental, regulatory, or administrative authority or any court, tribunal, or judicial, or arbitral body, and no other legal restraint or prohibition shall be in effect, preventing the purchase by the Purchaser of the Forward Purchase Units.

8. Termination. This Agreement may be terminated at any time prior to the Forward Closing:

(a) by mutual written consent of the Company and the Purchaser;

(b) automatically

(i) if the IPO is not consummated on or prior to twelve months from the date of this Agreement; or

(ii) if the Business Combination is not consummated within 24 months from the closing of the IPO, or such later date as may be approved by the Company’s stockholders.

In the event of any termination of this Agreement pursuant to this Section 8, the Forward Purchase Price (and interest thereon, if any), if previously paid, and all Purchaser’s funds paid in connection herewith shall be promptly returned to the Purchaser, and thereafter this Agreement shall forthwith become null and void and have no effect, without any liability on the part of the Purchaser or the Company and their respective directors, officers, employees, partners, managers, members, or stockholders and all rights and obligations of each party shall cease; provided, however, that nothing contained in this Section 8 shall relieve either party from liabilities or damages arising out of any fraud or willful breach by such party of any of its representations, warranties, covenants or agreements contained in this Agreement.

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9. General Provisions.

(a) Notices. All notices and other communications given or made pursuant to this Agreement shall be in writing and shall be deemed effectively given upon the earlier of actual receipt, or (i) personal delivery to the party to be notified, (ii) when sent, if sent by electronic mail or facsimile (if any) during normal business hours of the recipient, and if not sent during normal business hours, then on the recipient’s next Business Day, (iii) five (5) Business Days after having been sent by registered or certified mail, return receipt requested, postage prepaid, or (iv) one (1) Business Day after deposit with a nationally recognized overnight courier, freight prepaid, specifying next Business Day delivery, with written verification of receipt. All communications sent to the Company shall be sent to: Hudson Executive Investment Corp. III, 570 Lexington Avenue, 35th Floor, New York, New York 10022, Attn: Jonathan Dobres, Chief Financial Officer, email: ***@***, with a copy to the Company’s counsel at: Milbank LLP, 55 Hudson Yards, New York, New York 10001, Attn: Rod Miller, Esq., email: ***@***.

All communications to the Purchaser shall be sent to the Purchaser’s address as set forth on the signature page hereof, or to such e-mail address, facsimile number (if any) or address as subsequently modified by written notice given in accordance with this Section 9(a).

(b) No Finder’s Fees. Each party represents that it neither is nor will be obligated for any finder’s fee or commission in connection with this transaction. The Purchaser agrees to indemnify and to hold harmless the Company from any liability for any commission or compensation in the nature of a finder’s or broker’s fee arising out of this transaction (and the costs and expenses of defending against such liability or asserted liability) for which the Purchaser or any of its officers, employees or representatives is responsible. The Company agrees to indemnify and hold harmless the Purchaser from any liability for any commission or compensation in the nature of a finder’s or broker’s fee arising out of this transaction (and the costs and expenses of defending against such liability or asserted liability) for which the Company or any of its officers, employees or representatives is responsible.

(c) Survival of Representations and Warranties. All of the representations and warranties contained herein shall survive the Forward Closing.

(d) Entire Agreement. This Agreement, together with any documents, instruments and writings that are delivered pursuant hereto or referenced herein, constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

(e) Successors. All of the terms, agreements, covenants, representations, warranties, and conditions of this Agreement are binding upon, and inure to the benefit of and are enforceable by, the parties hereto and their respective successors. Nothing in this Agreement, express or implied, is intended to confer upon any party other than the parties hereto or their respective successors and assigns any rights, remedies, obligations or liabilities under or by reason of this Agreement, except as expressly provided in this Agreement.

(f) Assignments. Except as otherwise specifically provided herein, no party hereto may assign either this Agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the other party.

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(g) Counterparts. This Agreement may be executed in two or more counterparts, each of which will be deemed an original but all of which together will constitute one and the same instrument.

(h) Headings. The section headings contained in this Agreement are inserted for convenience only and will not affect in any way the meaning or interpretation of this Agreement.

(i) Governing Law. This Agreement, the entire relationship of the parties hereto, and any dispute between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of laws principles.

(j) Jurisdiction. The parties (i) hereby irrevocably and unconditionally submit to the jurisdiction of the state courts of New York and to the jurisdiction of the United States District Court for the Southern District of New York for the purpose of any suit, action or other proceeding arising out of or based upon this Agreement, (ii) agree not to commence any suit, action or other proceeding arising out of or based upon this Agreement except in state courts of New York or the United States District Court for the Southern District of New York, and (iii) hereby waive, and agree not to assert, by way of motion, as a defense, or otherwise, in any such suit, action or proceeding, any claim that it is not subject personally to the jurisdiction of the above-named courts, that its property is exempt or immune from attachment or execution, that the suit, action or proceeding is brought in an inconvenient forum, that the venue of the suit, action or proceeding is improper or that this Agreement or the subject matter hereof may not be enforced in or by such court.

(k) Waiver of Jury Trial. The parties hereto hereby waive any right to a jury trial in connection with any litigation pursuant to this Agreement and the transactions contemplated hereby.

(l) Amendments. This Agreement may not be amended, modified or waived as to any particular provision except with the prior written consent of the Company and the Purchaser.

(m) Severability. The provisions of this Agreement will be deemed severable and the invalidity or unenforceability of any provision will not affect the validity or enforceability of the other provisions hereof; provided, that if any provision of this Agreement, as applied to any party hereto or to any circumstance, is adjudged by a governmental authority, arbitrator, or mediator not to be enforceable in accordance with its terms, the parties hereto agree that the governmental authority, arbitrator, or mediator making such determination will have the power to modify the provision in a manner consistent with its objectives such that it is enforceable, and/or to delete specific words or phrases, and in its reduced form, such provision will then be enforceable and will be enforced.

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(n) Expenses. Each of the Company and the Purchaser will bear its own costs and expenses incurred in connection with the preparation, execution and performance of this Agreement and the consummation of the transactions contemplated hereby, including all fees and expenses of agents, representatives, financial advisors, legal counsel and accountants. The Company shall be responsible for the fees of its transfer agent; stamp taxes and all of The Depository Trust Company’s fees associated with the issuance of the Forward Purchase Securities and the securities issuable upon conversion or exercise of the Forward Purchase Securities.

(o) Construction. The parties hereto have participated jointly in the negotiation and drafting of this Agreement. If an ambiguity or question of intent or interpretation arises, this Agreement will be construed as if drafted jointly by the parties hereto and no presumption or burden of proof will arise favoring or disfavoring any party hereto because of the authorship of any provision of this Agreement. Any reference to any federal, state, local, or foreign law will be deemed also to refer to law as amended and all rules and regulations promulgated thereunder, unless the context requires otherwise. The words “include,” “includes,” and “including” will be deemed to be followed by “without limitation.” Pronouns in masculine, feminine, and neuter genders will be construed to include any other gender, and words in the singular form will be construed to include the plural and vice versa, unless the context otherwise requires. The words “this Agreement,” “herein,” “hereof,” “hereby,” “hereunder,” and words of similar import refer to this Agreement as a whole and not to any particular subdivision unless expressly so limited. The parties hereto intend that each representation, warranty, and covenant contained herein will have independent significance. If any party hereto has breached any representation, warranty, or covenant contained herein in any respect, the fact that there exists another representation, warranty or covenant relating to the same subject matter (regardless of the relative levels of specificity) which such party hereto has not breached will not detract from or mitigate the fact that such party hereto is in breach of the first representation, warranty, or covenant.

(p) Waiver. No waiver by any party hereto of any default, misrepresentation, or breach of warranty or covenant hereunder, whether intentional or not, may be deemed to extend to any prior or subsequent default, misrepresentation, or breach of warranty or covenant hereunder or affect in any way any rights arising because of any prior or subsequent occurrence.

(q) Specific Performance. The Purchaser agrees that irreparable damage may occur in the event any provision of this Agreement was not performed by the Purchaser in accordance with the terms hereof and that the Company shall be entitled to specific performance of the terms hereof, in addition to any other remedy at law or equity.

[Signature Page Follows]

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IN WITNESS WHEREOF, the undersigned have executed this Agreement to be effective as of the date first set forth above.

Address for Notices: 570 Lexington Avenue, 35th Floor

    New York, NY 10022

E-mail: ***@***

COMPANY:

HUDSON EXECUTIVE INVESTMENT CORP. III

[Signature Page to Forward Purchase Agreement]

TO BE EXECUTED UPON ANY ASSIGNMENT AND/OR REVISION IN ACCORDANCE WITH THIS AGREEMENT TO “NUMBER OF FORWARD PURCHASE UNITS” AND “AGGREGATE PURCHASE PRICE FOR FORWARD PURCHASE UNITS” SET FORTH BELOW

Number of Forward Purchase Units and Aggregate Purchase Price for Forward Purchase Units as of , 202[ ], accepted and agreed to as of this day of , 202[ ].

SCHEDULE A

SCHEDULE OF TRANSFERS OF FORWARD PURCHASE UNITS

The following transfers of a portion of the original number of Forward Purchase Units have been made:

A-1

TO BE EXECUTED UPON ANY ASSIGNMENT OR FINAL DETERMINATION OF FORWARD PURCHASE UNITS:

Schedule A as of , 202[ ], accepted and agreed to as of this day of , 202[ ] by:

A-2