Radiation Exposure Compensation Act Amendments of 2021 This bill expands two programs that compensate individuals who were exposed to radiation during certain nuclear testing or uranium mining and subsequently developed medical conditions, including cancers. First, the bill expands and extends a program that compensates individuals who were exposed to radiation from atmospheric nuclear testing or other sources and subsequently developed specified cancers. Under current law, this program compensates individuals who were present in a designated geographic area during a period of nuclear testing and certain individuals employed in uranium mining. The bill expands the designated areas to include Colorado, Idaho, Montana, New Mexico, and Guam and additional areas in Arizona, Nevada, and Utah; makes more individuals who worked in uranium mining eligible for the program; increases the amount of compensation awarded to and provides medical benefits for eligible claimants; and extends for 19 years following the bill's enactment the fund that supports this program and the statute of limitations for filing claims (currently, the program terminates on July 10, 2022). Second, the bill makes certain individuals employed in uranium mines or mills eligible for a program that compensates workers, including Department of Energy employees and contractors, for illnesses caused by occupational exposure to radiation and hazardous substances during development and testing of the nation's nuclear weapons stockpile. The bill also establishes a grant program in the National Institute of Environmental Health Sciences for institutions of higher education to study the epidemiological impacts of uranium mining and milling among individuals without occupational exposure.