Form of Letter Agreement from each of the Registrants initial stockholders, officers and directors

Exhibit 10.4

[______________, 202_]

Adit EdTech Acquisition Corp.

1345 Avenue of the Americas, 33^rd Floor

New York, NY 10105

EarlyBirdCapital, Inc.

366 Madison Avenue, 8^th Floor

New York, New York 10017

Gentlemen:

This letter agreement is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”) entered into by and between Adit EdTech Acquisition Corp., a Delaware corporation (the “Company”), and EarlyBirdCapital, Inc. as representative (the “Representative”) of the underwriters named in Schedule I thereto (the “Underwriters”), relating to an underwritten initial public offering (the “IPO”) of the Company’s units (the “Units”), each comprised of one share of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), and one-half of one warrant, each whole warrant exercisable for one (1) share of Common Stock (each, a “Warrant”). Certain capitalized terms used herein are defined in Section 12 hereof.

In order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the IPO, and in recognition of the benefit that such IPO will confer upon the undersigned, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the undersigned hereby agrees with the Company as follows:

1. If the Company solicits approval of its stockholders of a Business Combination, the undersigned will vote all shares of Common Stock (including (a) the Founders’ Common Stock and (b) the Private Shares) beneficially owned by him/her/it, whether acquired before, in or after the IPO, in favor of such Business Combination.

2. In the event that the Company fails to consummate a Business Combination within the time period set forth in the Company’s Amended and Restated Certificate of Incorporation, as the same may be amended from time to time (the “Certificate of Incorporation”), the undersigned will, as promptly as possible, cause the Company to (a) cease all operations except for the purpose of winding up, (b) as promptly as reasonably possible, but not more than ten (10) business days thereafter, redeem the IPO Shares, at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the Trust Account net of interest released to the Company as permitted pursuant to the Trust Agreement (less any income or other taxes payable and less up to $100,000 of interest to pay dissolution expenses), divided by the number of then outstanding IPO Shares, which redemption will completely extinguish public stockholders’ rights as stockholders (including the right to receive further liquidation distributions,

if any), subject to applicable law, and (c) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining stockholders and the Company’s board of directors, dissolve and liquidate, subject in the cases of clauses (b) and (c) to the Company’s obligations under Delaware law to provide for claims of creditors and other requirements of applicable law. The undersigned hereby waives any and all right, title, interest or claim of any kind in or to any distribution of the Trust Account (“Claim”) with respect to the shares of Founders’ Common Stock and Private Shares owned by the undersigned and hereby waives any Claim the undersigned may have in the future as a result of, or arising out of, any contracts or agreements with the Company and will not seek recourse against the Trust Account for any reason whatsoever. In the event of the liquidation of the Trust Account, Adit EdTech Sponsor, LLC (the “Sponsor”) agrees to indemnify and hold harmless the Company for any debts and obligations to target businesses or vendors or other entities that are owed money by the Company for services rendered or contracted for or products sold to the Company, but only to the extent necessary to ensure that such debt or obligation does not reduce the amount of funds in the Trust Account below $10.00 per share; provided that such indemnity shall not apply (i) if such vendor or prospective target business executed an agreement waiving any right, title, interest or claim of any kind they may have in or to any monies held in the Trust Account, or (ii) as to any claims under the Company’s obligation to indemnify the Underwriters against certain liabilities, including liabilities under the Securities Act of 1933, as amended (the “Securities Act”). The undersigned acknowledges and agrees that there will be no distribution from the Trust Account with respect to any Warrants, all rights of which will terminate on the Company’s liquidation.

3. The undersigned acknowledges and agrees that prior to entering into a Business Combination with a target business that is affiliated with any Insiders of the Company or their affiliates, such transaction must be approved by a majority of the Company’s disinterested and independent directors and the Company must obtain an opinion from an independent investment banking firm, or another independent entity that commonly renders valuation opinions, that such Business Combination is fair to the Company (or its stockholders) from a financial point of view.

4. Neither the undersigned nor any affiliate of the undersigned will be entitled to receive and will not accept any compensation or other cash payment, including any finder fee, prior to, or for services rendered in order to effectuate, the consummation of the Business Combination; provided that the Company shall be allowed to make the payments set forth in the Prospectus under the caption “Certain Relationships and Related Party Transactions”.

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(a) To the extent that the Underwriters do not exercise their over-allotment option to purchase up to an additional 3,000,000 Units in full within forty-five (45) days from the date of the Prospectus (and as further described in the Prospectus), the Sponsor agrees to forfeit, at no cost, a number of shares of Founder Common Stock in the aggregate equal to 750,000 multiplied by a fraction, (i) the numerator of which is 3,000,000 minus the number of Units purchased by the Underwriters upon the exercise of their over-allotment option, and (ii) the denominator of which is 3,000,000. The Sponsor will be required to forfeit only that number of shares of Founder Common Stock as is necessary so that the Insiders will own an aggregate of 20.0% of the Company’s issued and outstanding shares of capital stock after the IPO (not including the Private Shares).

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(b) The undersigned agrees that the shares of Founders’ Common Stock may not be transferred, assigned or sold (except to certain permitted transferees as described in the Registration Statement) until the earlier to occur of: (i) one (1) year after the consummation of an initial Business Combination, and (ii) the date following the completion of the Company’s initial Business Combination on which the Company completes a liquidation, merger, share exchange or other similar transaction that results in all of its public stockholders having the right to exchange their shares of Common Stock for cash, securities or other property. Notwithstanding the foregoing, if the closing price of the Common Stock equals or exceeds $12.00 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations and the like) for any twenty (20) trading days within any thirty (30) trading day period commencing at least one hundred fifty (150) days after the Company’s initial Business Combination, the shares of Founders’ Common Stock will be released from the lockup.

(c) The undersigned will not, without the prior written consent of the Representative pursuant to the Underwriting Agreement, offer, sell, contract to sell, pledge, hedge or otherwise dispose of (or enter into any transaction that is designed to, or might reasonably be expected to, result in the disposition (whether by actual disposition or effective economic disposition due to cash settlement or otherwise) by the undersigned or any affiliate of the undersigned or any person in privity with the undersigned or any affiliate of the undersigned), directly or indirectly, including the filing (or participation in the filing) of a registration statement with the Securities and Exchange Commission in respect of, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Securities and Exchange Commission promulgated thereunder with respect to, any other Units, Common Stock, Warrants of the Company or any securities convertible into, or exercisable, or exchangeable for, Common Stock or publicly announce an intention to effect any such transaction, for a period of one hundred and eighty (180) days after the date of the Underwriting Agreement.

(d) The undersigned agrees that until the Company consummates a Business Combination, the undersigned’s Private Securities will be subject to the transfer restrictions described in the agreement relating to the undersigned’s purchase of Private Securities.

6. The undersigned’s FINRA Questionnaire previously furnished to the Company and the Representative are true and accurate in all respects. The undersigned represents and warrants that:

(a) he/she/it has never had a petition under the federal bankruptcy laws or any state insolvency law been filed by or against (i) him/her/it or any partnership in which he/she/it was a general partner at or within two years before the time of filing; or (ii) any corporation or business association of which he/she was an executive officer at or within two years before the time of such filing;

(b) he/she/it has never had a receiver, fiscal agent or similar officer been appointed by a court for his/her/its business or property, or any such partnership;

(c) he/she/it has never been convicted of fraud in a civil or criminal proceeding;

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(d) he/she/it has never been convicted in a criminal proceeding or named the subject of a pending criminal proceeding (excluding traffic violations and minor offenses);

(e) he/she/it has never been the subject of any order, judgment or decree, not subsequently reversed, suspended or vacated, of any court of competent jurisdiction, permanently or temporarily enjoining or otherwise limiting him/her/it from (i) acting as a futures commission merchant, introducing broker, commodity trading advisor, commodity pool operator, floor broker, leverage transaction merchant, any other person regulated by the Commodity Futures Trading Commission (“CFTC”) or an associated person of any of the foregoing, or as an investment adviser, underwriter, broker or dealer in securities, or as an affiliated person, director or employee of any investment company, bank, savings and loan association or insurance company, or from engaging in or continuing any conduct or practice in connection with any such activity; or (ii) engaging in any type of business practice, or (iii) engaging in any activity in connection with the purchase or sale of any security or commodity or in connection with any violation of federal or state securities or federal commodities laws;

(f) he/she/it has never been the subject of any order, judgment or decree, not subsequently reversed, suspended or vacated, of any federal or state authority barring, suspending or otherwise limiting for more than sixty (60) days his/her/its right to engage in any activity described in Section 6(e)(i) above, or to be associated with persons engaged in any such activity;

(g) he/she/it has never been found by a court of competent jurisdiction in a civil action or by the SEC to have violated any federal or state securities law, where the judgment in such civil action or finding by the SEC has not been subsequently reversed, suspended or vacated;

(h) he/she/it has never been found by a court of competent jurisdiction in a civil action or by the CFTC to have violated any federal commodities law, where the judgment in such civil action or finding by the CFTC has not been subsequently reversed, suspended or vacated;

(i) he/she/it has never been the subject of, or a party to, any Federal or State judicial or administrative order, judgment, decree or finding, not subsequently reversed, suspended or vacated, relating to an alleged violation of (i) any Federal or State securities or commodities law or regulation, (ii) any law or regulation respecting financial institutions or insurance companies including, but not limited to, a temporary or permanent injunction, order of disgorgement or restitution, civil money penalty or temporary or permanent cease-and desist order, or removal or prohibition order or (iii) any law or regulation prohibiting mail or wire fraud or fraud in connection with any business entity;

(j) he/she/it has never been the subject of, or party to, any sanction or order, not subsequently reversed, suspended or vacated, or any self-regulatory organization, any registered entity, or any equivalent exchange, association, entity or organization that has disciplinary authority over its members or persons associated with a member;

(k) he/she/it has never been convicted of any felony or misdemeanor: (i) in connection with the purchase or sale of any security, (ii) involving the making of any false filing with the SEC, or (iii) arising out of the conduct of the business of an underwriter, broker, dealer, municipal securities dealer, investment advisor or paid solicitor of purchasers of securities;

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(l) he/she/it was never subject to a final order of a state securities commission (or an agency of officer of a state performing like functions); a state authority that supervises or examines banks, savings associations, or credit unions; a state insurance commission (or an agency or officer of a state performing like functions); an appropriate federal banking agency; the Commodity Futures Trading Commission; or the National Credit Union Administration that is based on a violation of any law or regulation that prohibits fraudulent, manipulative, or deceptive conduct;

(m) he/she/it has never been subject to any order, judgment or decree of any court of competent jurisdiction, that, at the time of such sale, restrained or enjoined him/her/it from engaging or continuing to engage in any conduct or practice: (i) in connection with the purchase or sale of any security, (ii) involving the making of any false filing with the SEC, or (iii) arising out of the conduct of the business of an underwriter, broker, dealer, municipal securities dealer, investment adviser or paid solicitor of purchasers of securities;

(n) he/she/it has never been subject to any order of the SEC that orders it to cease and desist from committing or causing a future violation of: (i) any scienter-based anti-fraud provision of the federal securities laws, including, but not limited to, Section 17(a)(1) of the Securities Act, Section 10(b) of the Exchange Act and Rule 10b-5 thereunder, and Section 206(1) of the Advisers Act or any other rule or regulation thereunder, or (ii) Section 5 of the Securities Act;

(o) he/she/it has never been named as an underwriter in any registration statement or Regulation A offering statement filed with the SEC that was the subject of a refusal order, stop order, or order suspending the Regulation A exemption, or is, currently, the subject of an investigation or proceeding to determine whether a stop order or suspension order should be issued;

(p) he/she/it has never been subject to a United States Postal Service false representation order, or is currently subject to a temporary restraining order or preliminary injunction with respect to conduct alleged by the United States Postal Service to constitute a scheme or device for obtaining money or property through the mail by means of false representations;

(q) he/she/it is not subject to a final order of a state securities commission (or an agency of officer of a state performing like functions); a state authority that supervises or examines banks, savings associations, or credit unions; a state insurance commission (or an agency or officer of a state performing like functions); an appropriate federal banking agency; the Commodity Futures Trading Commission; or the National Credit Union Administration that bars the undersigned from: (i) association with an entity regulated by such commission, authority, agency or officer, (ii) engaging in the business of securities, insurance or banking, or (iii) engaging in savings association or credit union activities;

(r) he/she/it is not subject to an order of the SEC entered pursuant to section 15(b) or 15B(c) of the Exchange Act or section 203(e) or 203(f) of the Investment Advisers Act of 1940 that: (i) suspends or revokes the undersigned’s registration as a broker, dealer, municipal securities dealer or investment adviser, (ii) places limitations on the activities, functions or operations of, or imposes civil money penalties on, such person, or (iii) bars the undersigned from being associated with any entity or from participating in the offering of any penny stock; and

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(s) he/she/it has never been suspended or expelled from membership in, or suspended or barred from association with a member of, a securities self-regulatory organization (e.g., a registered national securities exchange or a registered national or affiliated securities association) for any act or omission to act constituting conduct inconsistent with just and equitable principles of trade.

7. The undersigned has full right and power, without violating any agreement by which he/she/it is bound, to enter into this letter agreement.

8. The undersigned hereby waives any right to exercise redemption rights with respect to any shares of the Company’s common stock owned or to be owned by the undersigned, directly or indirectly (or to sell such shares to the Company in a tender offer), whether such shares be part of the Founders’ Common Stock, Private Shares or shares purchased by the undersigned in the IPO or in the aftermarket, and agrees not to seek redemption with respect to such shares in connection with any vote to approve a Business Combination (or sell such shares to the Company in a tender offer in connection with such a Business Combination).

9. The undersigned hereby agrees to not propose, or vote in favor of, an amendment to the Company’s Certificate of Incorporation that would affect the ability of holders of IPO Shares to redeem or sell their shares to the Company in connection with a Business Combination or affect the substance or timing of the Company’s obligation to redeem 100% of the IPO Shares if the Company does not complete a Business Combination within the time period required by the Certificate of Incorporation unless the Company provides public stockholders with the opportunity to redeem their IPO Shares upon such approval in accordance with the Certificate of Incorporation.

10. Each of the undersigned who is an officer of the Company hereby agrees not to become an officer or director of any other special purpose acquisition company which has publicly filed a registration statement with the SEC until (a) the Company has entered into a definitive agreement regarding the Company’s initial Business Combination, or (b) the Company has failed to consummate an initial Business Combination within 24 months after the consummation of the IPO.

11. This letter agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The undersigned hereby (i) agrees that any action, proceeding or claim against him/her/it arising out of or relating in any way to this letter agreement (a “Proceeding”) shall be brought and enforced in the courts of the State of New York of the United States of America for the Southern District of New York, and irrevocably submits to such jurisdiction, which jurisdiction shall be exclusive, and (ii) waives any objection to such exclusive jurisdiction or that such courts represent an inconvenient forum.

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12. As used herein, (a) “Business Combination” means a merger, share exchange, asset acquisition, stock purchase, recapitalization, reorganization or other similar business combination with one or more businesses or entities; (b) “Insiders” means all officers, directors, industry advisors, and the Sponsor immediately prior to the IPO; (c) “Founders’ Common Stock” means all of the shares of Common Stock of the Company acquired by an Insider prior to the IPO; (d) “IPO Shares” means the shares of Common Stock issued in the IPO; (e) “Private Units” means the units and underlying shares of Common Stock (“Private Shares”) and warrants (“Private Unit Warrants”) that are being sold privately by the Company simultaneously with the consummation of the IPO, if any; (f) “Private Warrants” means the warrants that are being sold privately by the Company simultaneously with the consummation of the IPO; (g) “Private Securities” means the Private Units and Private Warrants; (h) “Trust Account” means the trust account into which a portion of the net proceeds of the IPO will be deposited; (i) “Registration Statement” means the Company’s registration statement on Form S-1 (SEC File No. 333- [________]) filed with the Securities and Exchange Commission; and (j) “Prospectus” means the final prospectus of the Company dated [_______], 2020 as filed with the Securities Exchange Commission pursuant to Rule 424(b) under the Securities Act.

13. This letter agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof 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. This letter agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by all parties hereto.

14. The undersigned acknowledges and understands that the Underwriters and the Company will rely upon the agreements, representations and warranties set forth herein in proceeding with the IPO. The Company and the undersigned hereby acknowledges and agrees that the Representative on behalf of the Underwriters is a third party beneficiary of this letter agreement. Nothing contained herein shall be deemed to render the Underwriters a representative of, or a fiduciary with respect to, the Company, its stockholders or any creditor or vendor of the Company with respect to the subject matter hereof.

15. The undersigned hereby agrees and acknowledges that: (a) the Underwriters and the Company would be irreparably injured in the event of a breach of the undersigned’s obligations under this letter agreement (b) monetary damages may not be an adequate remedy for such breach and (c) the Underwriters and the Company shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event of such breach.

16. This letter agreement shall be binding on the undersigned and his/her/its successors and assigns. This letter agreement shall terminate on the earlier of (a) the liquidation of the Trust Account and (b) the expiration of the transfer restrictions on the Founders’ Common Stock and Private Securities contained in Section 5 hereof; provided, that such termination shall not relieve the undersigned from liability for any breach of this agreement prior to its termination.

[Remainder of Page Intentionally Left Blank; Signature Page Follows]

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[Signature Page to Letter Agreement]