TRAJECTORY ALPHA ACQUISITION CORP. New York, New York 10005

Exhibit 10.8

TRAJECTORY ALPHA ACQUISITION CORP.

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[     ], 2021

Trajectory Alpha Sponsor LLC

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Re: Administrative Services Agreement

Ladies and Gentlemen:

This letter agreement by and between Trajectory Alpha Acquisition Corp., a Delaware corporation (the “Company”), and Trajectory Alpha Sponsor LLC, a Delaware limited liability company (the “Services Provider”), dated as of the date set forth above, will confirm our agreement that, commencing on the date that securities of the Company are first listed in connection with the Company’s initial public offering (the “Listing Date”) and continuing until the earlier of (x) the consummation by the Company of an initial business combination and (y) the Company’s liquidation (in each case, as described in the Company’s Registration Statement on Form S-1 (File No. 333-253967) filed with the Securities and Exchange Commission) (such earlier date, the “Termination Date”):

1. the Services Provider (and/or any of its affiliates designated by the Services Provider) shall make available, or cause to be made available, to the Company at ▇▇ ▇▇▇▇ ▇▇▇▇▇▇, #▇▇▇▇ ▇▇▇ ▇▇▇▇, ▇▇▇ ▇▇▇▇ ▇▇▇▇▇ (or any successor location or other existing office locations of the Services Provider and/or any of its affiliates), certain office space and administrative and secretarial support services as may be reasonably requested by the Company. In exchange therefor, the Company shall pay to the Services Provider the sum of $10,000 per month, commencing on the Listing Date and continuing monthly thereafter until the Termination Date; and

2. the Services Provider hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind or nature as a result of, or arising out of, this letter agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public stockholders of the Company and into which substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust Account”), and hereby irrevocably waives any Claim it presently has or may have in the future as a result of, or arising out of, this letter agreement, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever.

This letter agreement 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.

This letter agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by all parties hereto.

No party hereto may assign either this letter agreement or any of its rights, interests or obligations hereunder without the prior written approval of the other party; provided, however, that the Services Provider may assign this letter agreement or any of its rights, interests or obligations hereunder to an affiliate without the prior written approval of the Company. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

This letter agreement constitutes the entire relationship of the parties hereto with respect to the subject matter described herein, and any litigation between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by and construed in accordance with, and interpreted pursuant to, the laws of the State of New York, without giving effect to its choice of law principles.

This letter agreement may be executed in one or more counterparts, each of which shall for all purposes be deemed to be an original, but all of which together shall constitute one and the same letter agreement.

[Signature Page Follows]

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Very truly yours,

TRAJECTORY ALPHA ACQUISITION CORP.

By:

Name:

Title:

AGREED TO AND ACCEPTED BY:

TRAJECTORY ALPHA SPONSOR LLC

By:

Name:

Title:

[Signature Page to Administrative Services Agreement—Trajectory Alpha Acquisition Corp.]