Exhibit 24

                                   POWER OF ATTORNEY

        KNOW ALL BY THESE PRESENTS, that the undersigned hereby makes,
constitutes and appoints Samuel Katz and Sheera Michael, acting singly and with
full power of substitution or revocation, the undersigned's true and lawful
attorneys-in-fact, with full power and authority as hereinafter described on
behalf of and in the name, place and stead of the undersigned to:

        (i)     execute for and on behalf of the undersigned, in the
                undersigned's capacity as a director, director nominee, officer
                or beneficial owner of ordinary shares of TZP Strategies
                Acquisition Corp., a Cayman Islands exempted company (the
                "Company"), any Schedule 13D or Schedule 13G, and any
                amendments, supplements or exhibits thereto (including any joint
                filing agreements) required to be filed by the undersigned under
                Section 13 of the Securities Exchange Act of 1934, as amended,
                and the rules promulgated thereunder (the "Exchange Act"), and
                any Forms 3, 4, and 5 and any amendments, supplements or
                exhibits thereto required to be filed by the undersigned under
                Section 16(a) of the Exchange Act;

        (ii)    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 schedules or forms and timely file such forms
                with the United States Securities and Exchange Commission and
                any applicable stock exchange; and

        (iii)   take any other action of any type whatsoever in connection with
                the foregoing which, in the opinion of such attorneys-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 attorneys-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
                attorneys-in-fact may approve in such attorneys-in-fact's
                discretion.

                The undersigned hereby grants to such attorneys-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
attorneys-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, or any liability for the failure to comply with, Section 13 and/or Section
16 of the Exchange Act.

        This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file reports or schedules under Section 13
or Section 16 of the Exchange Act with respect to the Company, unless earlier
revoked by the undersigned in a signed writing delivered to the foregoing
attorneys-in-fact.

                                     *  *  *  *  *

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 21st day of December, 2021.

                                        By: /s/ Stewart Wallace
                                           -------------------------------------
                                        Name: Stewart Wallace