POWER OF ATTORNEY

      Know all by these presents, that the undersigned hereby constitutes and
appoints each of the General Counsel, who is currently John Healy, and the Chief
Financial Officer, who is currently Esther van den Boom, and their respective
successors, signing singly, the undersigned's true and lawful attorney-in-fact
to:

      (1)   prepare, execute in the undersigned's name and on the undersigned's
      behalf, and submit to the U.S. Securities and Exchange Commission (the
      "SEC") a Form ID, including amendments thereto, and any other documents
      necessary or appropriate to obtain codes and passwords enabling the
      undersigned to make electronic filings with the SEC of reports required by
      Section 16(a) of the Securities Exchange Act of 1934 or any rule or
      regulation of the SEC;

      (2)   execute for and on behalf of the undersigned, in the undersigned's
      capacity as an officer and/or director of Tyra Biosciences, Inc., a
      Delaware corporation (the "Company") and/or beneficial owner of more than
      10% of the Company's capital stock, Forms 3, 4, and 5 and any amendments
      thereto in accordance with Section 16(a) of the Securities Exchange Act of
      1934 and the rules thereunder;

      (3)   do and perform any and all acts for and on behalf of the
      undersigned which may be necessary or desirable to complete and execute
      any such Form 3, 4, or 5, complete and execute any amendment or amendments
      thereto, and timely file such form with the SEC and any stock exchange or
      similar authority; and

      (4)   take any other action of any type whatsoever in connection with
      the foregoing which, in the opinion of such attorney-in-fact, may be of
      benefit to, in the best interest of, or legally required by, the
      undersigned, it being understood that the documents executed by such
      attorney-in-fact on behalf of the undersigned pursuant to this Power of
      Attorney shall be in such form and shall contain such terms and conditions
      as such attorney-in-fact may approve in such attorney-in-fact's
      discretion.

      The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this Power of Attorney and the rights and powers herein
granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934.

      The undersigned agrees that each such attorney-in-fact herein may rely
entirely on information furnished orally or in writing by the undersigned to
such attorney-in-fact.  The undersigned also agrees to indemnify and hold
harmless the Company and each such attorney-in-fact against an losses, claims,
damages or liabilities (or actions in these reports) that arise out of or are
based upon any untrue statements or omission of necessary facts in the
information provided by the undersigned to such attorney-in-fact for purposes of
executing, acknowledging, delivering or filing Forms 3, 4 or 5 (including
amendments thereto) or Form ID and agrees to reimburse the Company and such
attorney-in-fact for any legal or other expenses reasonably incurred in
connection with investigating or defending against any such loss, claim, damage,
liability or action.

      This Power of Attorney supersedes any power of attorney previously
executed by the undersigned regarding the purposes outlined in the first
paragraph hereof ("Prior Powers of Attorney"), and the authority of the
attorney-in-fact named in any Prior Powers of Attorney is hereby revoked.

      This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

                           [Signature Page to Follow]

      IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 14th day of September, 2021.


                                        /s/ Ron Swanson
                                        -------------------------------
                                        Name:  Ron Swanson