Frank Harrison, Elizabeth Peratrovich, and Miguel Trujillo Native American Voting Rights Act of 2021 This bill addresses the voting rights of Native American and Alaska Native voters and voting access on tribal lands. The bill includes provisions expanding the types of facilities that can be used as voter registration agencies; increasing polling site accessibility, including by expanding early in-person voting and providing ballot drop boxes; providing enforcement power to citizens and attorneys general; requiring approval for actions like moving a polling place; validating certain tribal identification for voting or registering to vote; permitting voters to designate another individual to return a ballot on their behalf; and expanding requirements for bilingual voting accessibility. In addition, the bill establishes a Native American voting task force grant program for the purpose of increasing voter outreach, education, registration, turnout, and accessibility for Native American communities. The bill also directs the Government Accountability Office to study and report on (1) the prevalence of nontraditional or nonexistent mailing addresses among Indians, members of tribes, and individuals residing on Indian lands; and (2) the alternatives for removing barriers to voter registration, receipt of voter information and materials, and receipt of ballots.