No Trace Act of 2021 This bill establishes a framework to prohibit federal, state, and local entities from obtaining geolocation information about U.S. persons without a warrant. At the federal level, it generally prohibits federal agencies from obtaining geolocation information about a U.S. person without first obtaining a warrant. State and local governments must generally have in effect substantially similar policies to be eligible for funds under the Edward Byrne Memorial Justice Assistance Grant program and the Community Oriented Policing Services program. Additionally, the bill directs the Government Accountability Office to study the compliance of federal agencies and state and local governments.