POWER OF ATTORNEY

        KNOW ALL BY THESE PRESENTS, that the undersigned hereby makes,
constitutes and appoints Timur Akazhanov and Richard Siegel, 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 H.I.G. 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 20th day of October, 2020.

                                        By: /s/ Brian Schwartz
                                            ------------------------
                                        Name: Brian Schwartz
                                        Title: Chief Executive Officer and
                                               Director