Redistricting Reform Act of 2021 This bill sets forth requirements for congressional redistricting. Specifically, the bill requires that congressional redistricting be conducted in accordance with a plan developed by (1) a state-established independent commission; or (2) if such a commission does not enact a plan, a three-judge panel from a U.S. District Court. This requirement does not apply to a state that has a plan developed and approved by an independent redistricting commission that complies with specified requirements. The bill outlines the criteria for a redistricting plan, including that the plan shall not unduly favor or disfavor any political party. Further, the bill establishes the requirements for appointing members to a state-established independent redistricting commission, including diversity requirements. The Government Accountability Office must report on the extent to which these commissions meet the diversity requirements. Next, the bill prohibits a state where the congressional districts have been redistricted from carrying out another redistricting until after the next apportionment of Representatives following a decennial census, unless a court requires the state to conduct a subsequent redistricting to comply with the Constitution, the Voting Rights Act of 1965, or the provisions of the bill. The bill also directs the Election Assistance Commission to make payments to states to carry out congressional redistricting.