Military Spouse Licensing Relief Act of 2021 This bill provides for the portability of professional licenses of service members and their spouses who are relocated, because of military orders, outside of the jurisdiction that issued the license. Specifically, a professional license in good standing of a service member or spouse shall be considered valid at a similar scope of practice and in the discipline applied for in the new jurisdiction for the duration of such military orders. To establish and maintain eligibility, a service member or spouse must (1) provide a copy of the military orders to the licensing authority in the new jurisdiction; (2) remain in good standing with the licensing authority that issued the license; and (3) submit to the authority of the licensing authority in the new jurisdiction for the purposes of standards of practice, discipline, and fulfillment of any continuing education requirements. The bill also provides that if a service member or spouse is licensed to operate in multiple jurisdictions through an interstate licensure compact, the service member or spouse is subject to the requirements of the compact or the applicable provisions of the state law rather than the provisions of this bill.