Investor Rights and Lock-Up Agreement

Exhibit 10.6

INVESTOR RIGHTS AND LOCK-UP AGREEMENT

THIS INVESTOR RIGHTS AND LOCK-UP AGREEMENT (this “Agreement”) is entered into as of July 14, 2023, by and among Carmell Therapeutics Corporation (f/k/a Alpha Healthcare Acquisition Corp. III), a Delaware corporation, (the “Company”) and the parties listed as Investors on Schedule I hereto (each, including any person or entity who hereinafter becomes a party to this Agreement pursuant to Section 8.2, an “Investor” and collectively, the “Investors”).

WHEREAS, Alpha Healthcare Acquisition Corp. III, a Delaware corporation (“ALPA”), Candy Merger Sub, Inc., a Delaware corporation (“Merger Sub”) and Carmell Therapeutics Corporation, a Delaware corporation (“Carmell”) have entered into that certain Business Combination Agreement, dated as of January 4, 2023 (as amended or supplemented from time to time, the “Business Combination Agreement”), pursuant to which, among other things, Merger Sub will merge with and into Carmell (the “Merger”), with Carmell surviving as a wholly owned subsidiary of ALPA;

WHEREAS, ALPA and AHAC Sponsor III LLC, a Delaware limited liability company (“Sponsor”), are parties to that certain Registration Rights Agreement, dated July 26, 2021 (the “Prior ALPA Agreement”);

WHEREAS, Carmell is party to that certain Third Amended and Restated Investors’ Rights Agreement, dated as of September 13, 2022, by and among Carmell and certain investors listed therein (the “Prior Carmell Agreement” and together with the Prior ALPA Agreement, the “Prior Agreements”);

WHEREAS, the Sponsor currently holds 3,861,026 shares of Class B common stock, par value $0.0001 per share, of ALPA issued by ALPA prior to the consummation of ALPA’s initial public offering (the “Founder Shares,” which for the sake of clarity shall continue to refer to such shares once converted into shares of Class A Common Stock on the Closing Date);

WHEREAS, the Founder Shares will automatically convert into Class A Common Stock at the time of the initial Business Combination (as defined in the Prior ALPA Agreement) on a one-for-one basis, subject to adjustment, on the terms and conditions provided in the ALPA Certificate of Incorporation;

WHEREAS, certain investors (“Carmell Investors”) hold (a) shares of common stock, par value $0.001 per share, of the Company (“Carmell Common Stock”); (b) shares designated as “Series A Convertible Preferred Stock” (“Carmell Series A Preferred Stock”); (c) shares designated as “Series B Convertible Preferred Stock” (“Carmell Series B Preferred Stock”); and (d) shares designated as “Series C Convertible Preferred Stock” (“Carmell Series C Preferred Stock” and together with Carmell Common Stock, Carmell Series A Preferred Stock and Carmell Series B Preferred Stock, the “Carmell Shares”);

WHEREAS, the Carmell Shares will be exchanged for Class A Common Stock on or about the date hereof, pursuant to the Business Combination Agreement; and

WHEREAS, ALPA and Carmell desire to terminate the Prior Agreements to provide for the terms and conditions included herein.

NOW, THEREFORE, in consideration of the mutual covenants and agreements set forth herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. DEFINITIONS. The following capitalized terms used herein have the following meanings:

“Addendum Agreement” is defined in Section 8.2.

“Agreement” is defined in the preamble to this Agreement.

“ALPA Certificate of Incorporation” means the Second Amended and Restated Certificate of Incorporation of Alpha Healthcare Acquisition Corp. III, effective as of March 22, 2021.

“ALPA Investors” shall mean the investors listed on Schedule I hereto.

“Business Combination Agreement” is defined in the preamble to this Agreement.

“Business Day” means a day other than a Saturday, Sunday or other day on which commercial banks in New York, New York are authorized or required by law to close.

“Carmell Common Stock” is defined in the recitals to this Agreement.

“Carmell Investors” is defined in the recitals to this Agreement.

“Carmell Series A Preferred Stock” is defined in the recitals to this Agreement.

“Carmell Series B Preferred Stock” is defined in the recitals to this Agreement.

“Carmell Series C Preferred Stock” is defined in the recitals to this Agreement.

“Carmell Shares” is defined in the recitals to this Agreement.

“Class A Common Stock” is defined in the recitals to this Agreement.

“Closing Date” is defined in the Business Combination Agreement.

“Commission” means the Securities and Exchange Commission, or any other Federal agency then administering the Securities Act or the Exchange Act.

“Company” is defined in the preamble to this Agreement.

“Exchange Act” means the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Commission promulgated thereunder, all as the same shall be in effect at the time.

“Founder Shares” is defined in the recitals to this Agreement.

“Investor” is defined in the preamble to this Agreement.

“Lock-up Period” is defined in Section 3.1.

“New Securities” means all shares of Class A Common Stock issued in connection with the Merger.

“Notices” is defined in Section 5.5.

“Permitted Transferee” means (i) the members of an Investor’s immediate family (for purposes of this Agreement, “immediate family” shall mean with respect to any natural person, any of the following: such person’s spouse, the siblings of such person and his or her spouse, and the direct descendants and ascendants (including adopted and step children and parents) of such person and his or her spouses and siblings); (ii) any trust or family limited liability company or partnership for the direct or indirect benefit of an Investor or the immediate family of an Investor; (iii) if an Investor is a trust, to the trustor or beneficiary of such trust or to the estate of a beneficiary of such trust; (iv) any officer, director, general partner, limited partner, shareholder, member, or owner of similar equity interests in an Investor; or (v) any affiliate of an Investor.

“Prior Agreements” is defined in the preamble to this Agreement.

“Prior ALPA Agreement” is defined in the preamble to this Agreement.

“Prior Carmell Agreement” is defined in the preamble to this Agreement.

“Registrable Securities” means (i) all shares of Class A Common Stock or Class B Common Stock held by an Investor prior to the Closing Date, or issuable upon the exercise of a warrant issued by the Company and held by an Investor prior to the Closing Date, (ii) New Securities and (iii) all shares of Class A Common Stock issued to any Investor with respect to such securities referenced in clauses (i) and (ii) by way of any share split, share dividend or other distribution, recapitalization, share exchange, share reconstruction, amalgamation, contractual control arrangement or similar event. As to any particular Registrable Securities, such securities shall cease to be Registrable Securities when: (a) a Registration Statement with respect to the sale of such securities shall have become effective under the Securities Act and such securities shall have been sold, transferred, disposed of or exchanged in accordance with such Registration Statement; (b) such securities shall have been otherwise transferred, new certificates for such securities not bearing a legend restricting further transfer shall have been delivered by the Company and subsequent public distribution of such securities shall not require registration under the Securities Act; or (c) such securities shall have ceased to be outstanding.

“Registration Statement” means a registration statement filed by the Company with the Commission in compliance with the Securities Act and the rules and regulations promulgated thereunder for a public offering and sale of equity securities, or securities or other obligations exercisable or exchangeable for, or convertible into, equity securities (other than a registration statement on Form S-4 or Form S-8, or their successors, or any registration statement covering only securities proposed to be issued in exchange for securities or assets of another entity).

“Securities Act” means the Securities Act of 1933, as amended, and the rules and regulations of the Commission promulgated thereunder, all as the same shall be in effect at the time.

“Transfer” means to (i) sell, offer to sell, contract or agree to sell, hypothecate, pledge, grant any option to purchase or otherwise dispose of or agree to dispose of, directly or indirectly, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Exchange Act, and the rules and regulations of the Commission promulgated thereunder, with respect to any shares of Class A Common Stock, (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any shares of Class A Common Stock, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (iii) publicly announce any intention to effect any transaction, including the filing of a registration statement specified in clause (i) or (ii), other than a Registration Statement filed pursuant to this Agreement. Notwithstanding the foregoing, a Transfer shall not be deemed to include any transfer for no consideration if the donee, trustee, heir or other transferee has agreed in writing to be bound by the same terms under this Agreement to the extent and for the duration that such terms remain in effect at the time of the Transfer.

2. UNDERWRITING AND DISTRIBUTION.

2.1 Rule 144. The Company covenants that it shall timely file any reports required to be filed by it under the Securities Act and the Exchange Act and shall take such further action as the holders of Registrable Securities may reasonably request, all to the extent required from time to time to enable such holders to sell Registrable Securities without registration under the Securities Act within the limitation of the exemptions provided by Rule 144 under the Securities Act, as such Rules may be amended from time to time, or any similar rule or regulation hereafter adopted by the Commission. Upon reasonable prior written request, the Company shall deliver to the Investors a customary written statement as to whether it has complied with such requirements.

3. LOCK-UP AGREEMENTS.

3.1 Investor Lock-Up. Each Investor agrees that it shall not Transfer any shares of Class A Common Stock or any securities convertible into or exercisable or exchangeable (directly or indirectly) for shares of Class A Common Stock (including New Securities) for a period of one year following the Closing Date (the “Lock-Up Period”); provided that each Investor shall have the right to Transfer $20,000 worth of Class A Common Stock held by such Investor as of the Closing. The foregoing restriction is expressly agreed to preclude each Investor during the Lock-up Period from engaging in any hedging or other transaction which is designed to or which reasonably could be expected to lead to or result in a sale or disposition of such Investor’s shares of Class A Common Stock even if such shares of Class A Common Stock would be disposed of by someone other than the undersigned. Such prohibited hedging or other transactions during the Lock-up Period would include without limitation any short sale or any purchase, sale or grant of any right (including, without limitation, any put or call option) with respect to any of the Investor’s shares of Class A Common Stock or with respect to any security that includes, relates to, or derives any significant part of its value from such shares of Class A Common Stock. The foregoing restrictions shall not apply to Transfers made: (i) pursuant to a bona fide gift or charitable contribution; (ii) by will or intestate succession upon the death of an Investor; (iii) to any Permitted Transferee; (iv) pursuant to a court order or settlement agreement related to the distribution of assets in connection with the dissolution of marriage or civil union; or (v) in the event of the Company’s completion of a liquidation, merger, share exchange or other similar transaction which results in all of its shareholders having the right to exchange their shares of Class A Common Stock for cash, securities or other property; provided that in the case of (i) or (iii), the recipient of such Transfer must enter into a written agreement agreeing to be bound by the terms of this Agreement, including the transfer restrictions set forth in this Section 3.1.

3.2 Sponsor Lock-Up. Sponsor agrees that it shall not Transfer any shares of Class A Common Stock or any securities convertible into or exercisable or exchangeable (directly or indirectly) for shares of Class A Common Stock (including New Securities) for a period of one year following the Closing Date. Sponsor further agrees that it shall not Transfer fifty percent (50%) of the Founder Shares until the earliest to occur of (x) five years from the Closing Date, (y) if the volume weighted average price (“VWAP”) of the Class A Common Stock on Nasdaq, or any other national securities exchange on which the Class A Common Stock is then traded, as reported by Bloomberg, L.P. is greater than or equal to $11.50 over any twenty (20) trading days within any thirty (30) trading day period following the Closing Date, then, commencing at least 150 days after the Closing Date, or (z) the date on which the Company completes a liquidation, merger, capital stock exchange, reorganization or other similar transaction that results in all of the Company’s stockholders having the right to exchange their shares of Class A Common Stock for cash, securities or other property. The foregoing restriction is expressly agreed to preclude Sponsor during the lock-up period from engaging in any hedging or other transaction which is designed to or which reasonably could be expected to lead to or result in a sale or disposition of Sponsor’s shares of Class A Common Stock even if such shares of Class A Common Stock would be disposed of by someone other than the undersigned. Such prohibited hedging or other transactions during the lock-up period would include without limitation any short sale or any purchase, sale or grant of any right (including, without limitation, any put or call option) with respect to any of Sponsor’s shares of Class A Common Stock or with respect to any security that includes, relates to, or derives any significant part of its value from such shares of Class A Common Stock. The foregoing restrictions shall not apply to Transfers made in the event of the Company’s completion of a liquidation, merger, share exchange or other similar transaction which results in all of its shareholders having the right to exchange their shares of Class A Common Stock for cash, securities or other property.

4. BOARD OF DIRECTORS.

4.1 Directors. At Closing, the ALPA Investors shall have the right, but not the obligation, to designate for election as a director of the Company, and the Company Board (including any Committee thereof) shall nominate (and recommend for election and include such recommendation in a timely manner in any proxy statement, consent solicitation or other applicable announcement to the Company’s shareholders) two (2) individuals to serve on the Company Board – one as Executive Chairman and one as independent director.

4.2 Director Indemnification. As promptly as reasonably practicable following the request of any director designated pursuant to Section 4.1, the Company shall enter into an indemnification agreement with the director, in the form entered into with the other members of the Company Board or, if not entered into by other members of the Company Board, a customary form. The Company shall pay the reasonable, documented and out-of-pocket expenses incurred by such director related to his or her service to the Company, including attending meetings of the Company Board or any Committee or sub-Committee thereof or events attended on behalf of the Company or any of its subsidiaries at the Company’s request. For so long as a director designated pursuant to Section 7.1 serves as a director of the Company, the Company shall not amend, alter or repeal any right to indemnification or exculpation covering or benefiting any director designated pursuant to Section 4.1 as and to the extent consistent with applicable law, including but not limited to under the Company’s certificate of incorporation (except to the extent such amendment or alteration permits the Company to provide broader indemnification or exculpation rights on a retroactive basis than permitted prior thereto). The Company shall (i) purchase directors’ and officers’ liability insurance in an amount determined by the Company Board to be reasonable and customary and (ii) for so long as any director designated pursuant to Section 4.1 serves as a director of the Company Board, maintain such coverage with respect to such director; provided that upon removal or resignation of such director for any reason, the Company shall take all actions reasonably necessary to extend such directors’ and officers’ liability insurance coverage for a period of not less than six (6) years from any such event in respect of any act or omission occurring at or prior to such event.

5. MISCELLANEOUS.

5.1 Other Registration Rights and Arrangements. The parties hereby terminate the Prior Agreements, each of which shall be of no further force and effect and is hereby superseded and replaced in its entirety by this Agreement. The Company shall not hereafter enter into any agreement with respect to its securities which is inconsistent with or violates the rights granted to the holders of Registrable Securities in this Agreement and in the event of any conflict between any such agreement or agreements and this Agreement, the terms of this Agreement shall prevail.

5.2 Assignment; No Third-Party Beneficiaries. This Agreement and the rights, duties and obligations of the Company hereunder may not be assigned or delegated by the Company in whole or in part. This Agreement and the rights, duties and obligations of the holders of Registrable Securities hereunder may be freely assigned or delegated by such holder of Registrable Securities in conjunction with and to the extent of any permitted transfer of Registrable Securities by any such holder to a Permitted Transferee. This Agreement and the provisions hereof shall be binding upon and shall inure to the benefit of each of the parties hereto and their respective successors and assigns and the holders of Registrable Securities and their respective successors and permitted assigns. This Agreement is not intended to confer any rights or benefits on any persons that are not party hereto other than as expressly set forth this Section 5.2. The rights of a holder of Registrable Securities under this Agreement may be transferred by such a holder to a transferee who acquires or holds Registrable Securities; provided, however, that such transferee has executed and delivered to the Company a properly completed agreement to be bound by the terms of this Agreement substantially in form attached hereto as Exhibit A (an “Addendum Agreement”), and the transferor shall have delivered to the Company no later than thirty (30) days following the date of the transfer, written notification of such transfer setting forth the name of the transferor, the name and address of the transferee, and the number of Registrable Securities so transferred. The execution of an Addendum Agreement shall constitute a permitted amendment of this Agreement.

5.3 Amendments and Modifications. Upon the written consent of the Company and the Holders of at least a majority in interest of the Registrable Securities at the time in question, compliance with any of the provisions, covenants and conditions set forth in this Agreement may be waived, or any of such provisions, covenants or conditions may be amended or modified; provided, however, that notwithstanding the foregoing, any amendment hereto or waiver hereof that adversely affects an Investor, solely in his, her or its capacity as a holder of the shares of capital stock of the Company, in a manner that is materially different from other Investors (in such capacity) shall require the consent of such Investor so affected. No course of dealing between any Investor or the Company and any other party hereto or any failure or delay on the part of an Investor or the Company in exercising any rights or remedies under this Agreement shall operate as a waiver of any rights or remedies of any Investor or the Company. No single or partial exercise of any rights or remedies under this Agreement by a party shall operate as a waiver or preclude the exercise of any other rights or remedies hereunder or thereunder by such party.

5.4 Term. This Agreement shall terminate upon the earlier of (i) the tenth anniversary of the date of this Agreement or (ii) the date as of which there shall be no Registrable Securities outstanding; provided further that with respect to any Investor, such Investor will have no rights under this Agreement and all obligations of the Company to such Investor under this Agreement shall terminate upon the earlier of (x) the date at least one year after the date hereof that such Investor ceases to hold at least 1 % of the Registrable Securities outstanding on the date hereof or (y) if such Investor is a director or an executive officer of the Company, the date such Investor no longer serves as a director or an executive officer of the Company.

5.5 Notices. All notices, demands, requests, consents, approvals or other communications (collectively, “Notices”) required or permitted to be given hereunder or which are given with respect to this Agreement shall be in writing and shall be personally served, delivered by reputable air courier service with charges prepaid, or transmitted by facsimile or email, addressed as set forth below, or to such other address as such party shall have specified most recently by written notice. Notice shall be deemed given (i) on the date of service or transmission if personally served or transmitted by email, telegram, telex or facsimile; provided, that if such service or transmission is not on a Business Day or is after normal business hours, then such notice shall be deemed given on the next Business Day or (ii) one Business Day after being deposited with a reputable courier service with an order for next-day delivery, to the parties as follows:

If to the Company:

Carmell Therapeutics Corporation

2403 Sidney Street, Suite 300

Pittsburgh, PA 15203

Attn: Randolph W. Hubbell

Email: ***@***

with a copy (which shall not constitute notice) to:

Troutman Pepper Hamilton Sanders LLP

400 Berwyn Park

899 Cassatt Road

Berwyn, PA 19312

Attn: Scott R. Jones

Email: [***]

If to ALPA:

c/o ALPA Healthcare Acquisition Corp. III

1177 Avenue of the Americas, 5th Floor

New York, NY 10036

Attn: Rajiv Shukla

Patrick Sturgeon

Email: [***]

with a copy (which shall not constitute notice) to:

Goodwin Procter LLP

100 Northern Avenue

Boston, MA 02210

Attn: Laurie A. Burlingame

Email: [***]

If to an Investor, to the address set forth under such Investor’s signature to this Agreement or to such Investor’s address as found in the Company’s books and records.

5.6 Severability. This Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible that is valid and enforceable.

5.7 Counterparts. This Agreement may be executed in multiple counterparts, each of which shall be deemed an original, and all of which taken together shall constitute one and the same instrument.

5.8 Entire Agreement. This Agreement (including all agreements entered into pursuant hereto and all certificates and instruments delivered pursuant hereto and thereto) constitute the entire agreement of the parties with respect to the subject matter hereof and supersede all prior and contemporaneous agreements, representations, understandings, negotiations and discussions between the parties, whether oral or written, including, without limitation the Prior Agreements.

IN WITNESS WHEREOF, the parties have caused this Investor Rights and Lock-Up Agreement to be executed and delivered by their duly authorized representatives as of the date first written above.

IN WITNESS WHEREOF, the parties have caused this Investor Rights and Lock Up Agreement to be executed and delivered by their duly authorized representatives as of the date first written above.

EXHIBIT A

Addendum Agreement

This Addendum Agreement (“Addendum Agreement”) is executed on __________________, 20___, by the undersigned (the “New Holder”) pursuant to the terms of that certain Investor Rights and Lock-Up Agreement dated as of July 14, 2023 (the “Agreement”), by and among the Company and the Investors identified therein, as such Agreement may be amended, supplemented or otherwise modified from time to time. Capitalized terms used but not defined in this Addendum Agreement shall have the respective meanings ascribed to such terms in the Agreement. By the execution of this Addendum Agreement, the New Holder agrees as follows:

1. Acknowledgment. New Holder acknowledges that New Holder is acquiring certain shares of common stock of the Company (the “Class A Common Stock”) as a transferee of such shares of Class A Common Stock from a party in such party’s capacity as a holder of Registrable Securities under the Agreement, and after such transfer, New Holder shall be considered an “Investor” and a holder of Registrable Securities for all purposes under the Agreement.

2. Agreement. New Holder hereby (a) agrees that the shares of Class A Common Stock shall be bound by and subject to the terms of the Agreement and (b) adopts the Agreement with the same force and effect as if the New Holder were originally a party thereto.

3. Notice. Any notice required or permitted by the Agreement shall be given to New Holder at the address or facsimile number listed below New Holder’s signature below.

SIGNATURE PAGE TO ADDENDUM AGREEMENT