Reporting Efficiently to Proper Officials in Response to Terrorism Act of 2021 or the REPORT Act This bill requires the primary government agency investigating an act of terrorism to submit to Congress an unclassified report within one year after the agency completes its investigation. The agency shall conduct such investigation in collaboration with the Department of Homeland Security (DHS), the Department of Justice (DOJ), the Federal Bureau of Investigation (FBI), and the National Counterterrorism Center. Such requirement shall not apply in instances in which DHS, DOJ, the FBI, or the center determines that the information required to be reported could jeopardize an ongoing investigation or prosecution, in which case the principal agency making such determination must notify Congress. Such a report shall (1) identify any gaps in national security that could be addressed to prevent future acts of terrorism, and (2) include any recommendations for additional measures that could be taken to improve homeland security.