EX-10.4





 Exhibit 10.4 

PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT 

THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT, dated as of December 9, 2021 (as amended, supplemented or otherwise modified from
time to time, this “Agreement”), is entered into by and between Trajectory Alpha Acquisition Corp., a Delaware corporation (the “Company”), and Trajectory Alpha Sponsor LLC, a Delaware limited
liability company (the “Purchaser”). 
 WHEREAS, the Company intends to consummate an initial public offering of the
Company’s units (the “Public Offering”), each unit consisting of one share of Class A common stock, par value $0.0001 per share (each, a “Share”), and
one-half of one redeemable warrant, each whole warrant exercisable for one Share at an exercise price of $11.50 per Share, as set forth in the Company’s Registration Statement on Form S-1, filed with the U.S. Securities and Exchange Commission (the “SEC”), File No. 333-253967 (the “Registration
Statement”), under the Securities Act of 1933, as amended (the “Securities Act”); and 
 WHEREAS, the
Purchaser now wishes to purchase, at a price of $1.00 per warrant, an aggregate of 5,500,000 private placement warrants (or up to 5,725,000 private placement warrants, depending on the extent to which the underwriters exercise their option to
purchase additional units) (the “Private Placement Warrants”), each Private Placement Warrant entitling the holder to purchase one Share at an exercise price of $11.50 per Share. 

NOW THEREFORE, IN CONSIDERATION OF the mutual promises contained in this Agreement and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as follows: 

AGREEMENT 

Section 1. Authorization, Purchase and Sale; Terms of the Private Placement Warrants. 

A. Authorization of the Private Placement Warrants. The Company has duly authorized the issuance and sale of the Private Placement
Warrants to the Purchaser. 
 B. Purchase and Sale of the Private Placement Warrants. 

(i) On the date of the consummation of the Public Offering, the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase
from the Company, 5,500,000 Private Placement Warrants (the “Initial Private Placement Warrants”) at a price of $1.00 per Private Placement Warrant for an aggregate purchase price of $5,500,000 (the “Purchase
Price”). The Purchaser shall pay the Purchase Price by wire transfer of immediately available funds in accordance with the Company’s wiring instructions at least one (1) business day prior to the effective date of the
Registration Statement, or on such other date as the Company and the Purchaser may agree. 












 (ii) In the event that the underwriters’ option to purchase additional units is
exercised in full, the Purchaser shall purchase up to an additional 225,000 Private Placement Warrants (the “Additional Private Placement Warrants”), in the same proportion as the amount of the option to purchase additional
units that is exercised and, simultaneously with such purchase of Additional Private Placement Warrants, as payment in full for the Additional Private Placement Warrants being purchased hereunder, and at least one (1) business day prior to the
closing of all or any portion of the option to purchase additional units, or on such other date as the Company and the Purchaser may agree, the Purchaser shall pay $1.00 per Additional Private Placement Warrant, up to an aggregate amount of
$225,000, by wire transfer of immediately available funds in accordance with the Company’s wiring instructions. 
 (iii) The closing of
the purchase and sale of the Initial Private Placement Warrants shall take place simultaneously with the closing of the Public Offering (the “Initial Closing Date”). The closing of the purchase and sale of the Additional
Private Placement Warrants, if applicable, shall take place simultaneously with the closing of all or any portion of the option to purchase additional units (such closing date, together with the Initial Closing Date, the “Closing
Dates” and, each, a “Closing Date”). The closing of the purchase and sale of each of the Initial Private Placement Warrants and the Additional Private Placement Warrants shall take place at the offices of Paul,
Weiss, Rifkind, Wharton & Garrison LLP, 1285 Avenue of the Americas, New York, New York, 10019, or such other place as may be agreed upon by the parties hereto. 

C. Terms of the Private Placement Warrants. 

(i) Each Private Placement Warrant shall have the terms set forth in that certain private warrant agreement to be entered into by the Company
and a warrant agent in connection with the Public Offering (the “Private Warrant Agreement”) and shall be subject to the terms of that certain letter agreement to be entered into by the Company, the Purchaser and the other
parties thereto in connection with the Public Offering. 
 (ii) At or prior to the Initial Closing Date, the Company and the Purchaser shall
enter into that certain registration rights agreement (the “Registration Rights Agreement”), pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Private Placement Warrants and
the Shares underlying the Private Placement Warrants. 
 Section 2. Representations and Warranties of the Company. As a material
inducement to the Purchaser to enter into this Agreement and purchase the Private Placement Warrants, the Company hereby represents and warrants to the Purchaser (which representations and warranties shall survive the Closing Dates) that: 

A. Incorporation and Corporate Power. The Company is a corporation duly incorporated, validly existing and in good standing under the
laws of the State of Delaware and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect on the financial condition, results of operations or assets of the
Company. The Company possesses all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement and the Private Warrant Agreement. 

  
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 B. Authorization; No Breach. 

(i) The execution, delivery and performance of this Agreement and the Private Placement Warrants have been duly authorized by the Company as of
the applicable Closing Date. This Agreement constitutes a valid and binding obligation of the Company, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of
general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law). Upon issuance in accordance with, and payment pursuant to, the terms of the Private
Warrant Agreement and this Agreement, the Private Placement Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms as of the applicable Closing Date. 

(ii) The execution and delivery by the Company of this Agreement and the Private Placement Warrants, the issuance and sale of the Private
Placement Warrants, the issuance of the Shares upon exercise of the Private Placement Warrants and the fulfillment of, and compliance with, the respective terms hereof and thereof by the Company, do not and will not as of the applicable Closing Date
(a) conflict with or result in a breach of the terms, conditions or provisions of, (b) constitute a default under, (c) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s capital stock
or assets under, (d) result in a violation of or (e) require any authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or agency
pursuant to the certificate of incorporation or the bylaws of the Company (in effect on the date hereof or as may be amended prior to completion of the Public Offering), or any material law, statute, rule or regulation to which the Company is
subject, or any agreement, order, judgment or decree to which the Company is subject, except for any filings required after the date hereof under federal or state securities laws. 

C. Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof, the Private Warrant Agreement and
the Company’s amended and restated certificate of incorporation, the Shares issuable upon exercise of the Private Placement Warrants will be duly and validly issued, fully paid and non-assessable. On the
date of issuance of the Private Placement Warrants, the Shares issuable upon exercise of the Private Placement Warrants shall have been reserved for issuance in accordance with the terms of this Agreement. Upon issuance in accordance with, and
payment pursuant to, the terms hereof and the Private Warrant Agreement, the Purchaser will have good title to the Private Placement Warrants purchased by it and the Shares issuable upon exercise of such Private Placement Warrants, free and clear of
all liens, claims and encumbrances of any kind, other than (i) transfer restrictions hereunder and under the other agreements contemplated hereby, (ii) transfer restrictions under federal and state securities laws, and (iii) liens,
claims or encumbrances imposed due to the actions of the Purchaser. 
 D. Governmental Consents. No permit, consent, approval or
authorization of, or declaration to or filing with, any governmental authority is required in connection with the execution, delivery and performance by the Company of this Agreement or the consummation by the Company of any other transactions
contemplated hereby. 

  
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 E. Regulation D Qualification. Neither the Company nor, to its knowledge, any of its
affiliates, officers, directors or beneficial stockholders of twenty percent (20%) or more of its outstanding securities, has experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act. 

Section 3. Representations and Warranties of the Purchaser. As a material inducement to the Company to enter into this Agreement
and issue and sell the Private Placement Warrants to the Purchaser, the Purchaser hereby represents and warrants to the Company (which representations and warranties shall survive the Closing Dates) that: 

A. Organization and Requisite Authority. The Purchaser possesses all requisite power and authority necessary to carry out the
transactions contemplated by this Agreement. 
 B. Authorization; No Breach. 

(i) This Agreement constitutes a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to
bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or
law). 
 (ii) The execution and delivery by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by
the Purchaser does not and shall not as of the applicable Closing Date (a) conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of, (b) constitute a default under, (c) result in the creation of
any lien, security interest, charge or encumbrance upon the Purchaser’s equity or assets under, (d) result in a violation of or (e) require any authorization, consent, approval, exemption or other action by or notice or declaration
to, or filing with, any court or administrative or governmental body or agency pursuant to the certificate of formation or the limited liability company agreement of the Purchaser (in effect on the date hereof or as may be amended prior to
completion of the Public Offering) or any material law, statute, rule or regulation to which the Purchaser is subject, or any agreement, instrument, order, judgment or decree to which the Purchaser is subject, except for any filings required after
the date hereof under federal or state securities laws. 
 C. Investment Representations. 

(i) The Purchaser is acquiring the Private Placement Warrants and, upon exercise of the Private Placement Warrants, the Shares issuable upon
such exercise (collectively, the “Securities”), for the Purchaser’s own account, for investment purposes only and not with a view towards, or for resale in connection with, any public sale or distribution thereof. 

(ii) The Purchaser is an “accredited investor” as such term is defined in Rule 501(a)(3) of Regulation D under the Securities Act and
the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act. 
  

  
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 (iii) The Purchaser understands that the Securities are being offered and will be sold to it
in reliance on specific exemptions from the registration requirements of the United States federal and state securities laws and that the Company is relying upon the truth and accuracy of, and the Purchaser’s compliance with, the
representations and warranties of the Purchaser set forth herein in order to determine the availability of such exemptions and the eligibility of the Purchaser to acquire such Securities. 

(iv) The Purchaser did not decide to enter into this Agreement as a result of any general solicitation or general advertising within the
meaning of Rule 502(c) of Regulation D under the Securities Act. 
 (v) The Purchaser has been furnished with all materials relating to the
business, finances and operations of the Company and materials relating to the offer and sale of the Securities which have been requested by the Purchaser. The Purchaser has been afforded the opportunity to ask questions of the executive officers
and directors of the Company. The Purchaser understands that its investment in the Securities involves a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed investment
decision with respect to the acquisition of the Securities. 
 (vi) The Purchaser understands that no United States federal or state agency
or any other government or governmental agency has passed on or made any recommendation or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such authorities passed upon or
endorsed the merits of the offering of the Securities. 
 (vii) The Purchaser understands that (a) the Securities have not been and are
not being registered under the Securities Act or any state securities laws, and may not be offered for sale, sold, assigned or transferred unless (1) subsequently registered thereunder or (2) sold in reliance on an exemption therefrom and
(b) except as specifically set forth in the Registration Rights Agreement, neither the Company nor any other person is under any obligation to register the Securities under the Securities Act or any state securities laws or to comply with the
terms and conditions of any exemption thereunder. In this regard, the Purchaser understands that the SEC has taken the position that the promoters or affiliates of a blank check company and their transferees, both before and after an initial
Business Combination, are deemed to be “underwriters” under the Securities Act when reselling the securities of a blank check company. Based on that position, Rule 144 promulgated under to the Securities Act would not be available for
resale transactions of the Securities despite technical compliance with the requirements of Rule 144 promulgated under to the Securities Act, and the Securities can be resold only through a registered offering or in reliance upon another exemption
from the registration requirements of the Securities Act. 
 (viii) The Purchaser has such knowledge and experience in financial and business
matters, knowledge of the high degree of risk associated with investments in the securities of companies in the development stage such as the Company, is capable of evaluating the merits and risks of an investment in the Securities and is able to
bear the economic risk of an investment in the Securities in the amount contemplated hereunder for an indefinite period of time. The Purchaser has adequate means of providing for its current financial needs and contingencies and will have no current
or anticipated future needs for liquidity which would be jeopardized by the investment in the Securities. The Purchaser can afford a complete loss of its investments in the Securities. 

 

  
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 (ix) The Purchaser understands that the Private Placement Warrants shall bear the legend
substantially in the form set forth in the Private Warrant Agreement. 
 Section 4. Conditions of the Purchaser’s
Obligations. The obligations of the Purchaser to purchase and pay for the Private Placement Warrants are subject to the fulfillment, on or before the Closing Dates, of each of the following conditions: 

A. Representations and Warranties. The representations and warranties of the Company contained in Section 2
shall be true and correct at and as of the applicable Closing Date as though then made. 
 B. Performance. The Company shall have
performed and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before the applicable Closing Date. 

C. Corporate Consents. The Company shall have obtained the consent of the Company’s board of directors authorizing the execution,
delivery and performance of this Agreement and the Private Warrant Agreement and the issuance and sale of the Private Placement Warrants hereunder. 

D. No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted,
entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the
transactions contemplated by this Agreement or the Private Warrant Agreement. 
 E. Private Warrant Agreement and Registration Rights
Agreement. The Company shall have entered into the Private Warrant Agreement with a warrant agent and the Registration Rights Agreement, in each case, on terms satisfactory to the Purchaser. 

Section 5. Conditions of the Company’s Obligations. The obligations of the Company to the Purchaser under this Agreement are
subject to the fulfillment, on or before the applicable Closing Date, of each of the following conditions: 
 A. Representations and
Warranties. The representations and warranties of the Purchaser contained in Section 3 shall be true and correct at and as of the applicable Closing Date as though then made. 

B. Performance. The Purchaser shall have performed and complied with all agreements, obligations and conditions contained in this
Agreement that are required to be performed or complied with by the Purchaser on or before the applicable Closing Date. 
 C. No
Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any
self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Private Warrant Agreement. 

 

  
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 D. Private Warrant Agreement. The Company shall have entered into the Private Warrant
Agreement with a warrant agent. 
 Section 6. Termination. This Agreement may be terminated by the Company or the Purchaser at
any time after December 31, 2021 upon written notice to the other party hereto if the closing of the Public Offering does not occur prior to such date. 

Section 7. Survival of Representations and Warranties. All of the representations and warranties contained herein shall survive
the applicable Closing Date. 
 Section 8. Definitions. Terms used but not otherwise defined in this Agreement shall have the
meaning assigned to such terms in the Registration Statement. 
 Section 9. Miscellaneous. 

A. Successors and Assigns. Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or
on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign
this Agreement, other than assignments by the Purchaser to affiliates thereof (including one or more of its members). 
 B.
Severability. Whenever possible, each provision of this Agreement shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under
applicable law, such provision shall be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement. 

C. Counterparts. This Agreement may be executed simultaneously in two or more counterparts, none of which need contain the signatures of
more than one party, but all such counterparts taken together shall constitute one and the same agreement. A signed copy of this Agreement delivered by facsimile, electronic mail or other means of electronic transmission shall be deemed to have the
same legal effect as delivery of an original signed copy of this Agreement. 
 D. Descriptive Headings; Interpretation. The
descriptive headings of this Agreement are inserted for convenience only and do not constitute a substantive part of this Agreement. The use of the word “including” in this Agreement shall be by way of example rather than by limitation.

 E. Governing Law. This Agreement and the rights and obligations of the parties hereunder shall be construed in accordance with and
governed by the laws of New York applicable to contracts wholly performed within the borders of such state, without giving effect to the conflict of law principles thereof. The parties hereto irrevocably submit to the exclusive jurisdiction of any
federal court sitting in the Southern District of New York or any state court located in New York County, State of New York, over any suit, action or proceeding arising out of or relating to this Agreement. To the fullest extent they may effectively
do so under applicable law, the parties hereto 

  
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irrevocably waive and agree not to assert, by way of motion, as a defense or otherwise, any claim that they are not subject to the jurisdiction of any such court, any objection that they may now
or hereafter have to the laying of the venue of any such suit, action or proceeding brought in any such court and any claim that any such suit, action or proceeding brought in any such court has been brought in an inconvenient forum. 

F. Amendments. This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument
executed by all parties hereto. 
 [Signature Page Follows] 

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

			
	TRAJECTORY ALPHA ACQUISITION CORP.
		
	By:	 	 /s/ Michael E.S. Frankel

		 	Name: Michael E.S. Frankel
		 	Title:   President and Chief Financial Officer
	
	TRAJECTORY ALPHA SPONSOR LLC
		
	By:	 	 /s/ Michael E.S. Frankel

		 	Name: Michael E.S. Frankel
		 	Title:   Managing Member


 [Signature Page to Private Placement Warrants Purchase Agreement—Trajectory Alpha Acquisition
Corp.]