Research Investment to Spark the Economy Act of 2021 or the RISE Act of 2021 This bill authorizes the Departments of Agriculture, Commerce, Defense, Education, Energy, the Interior, Health and Human Services, and Transportation, National Aeronautics and Space Administration (NASA), National Science Foundation, and Environmental Protection Agency to provide support for research regarding COVID-19 (i.e., coronavirus disease 2019) or research disrupted by the COVID-19 pandemic. Support may be used to provide supplemental funding to extend the duration of a grant to a research institution, national laboratory, or individual that was awarded prior to the enactment of this bill, or to expand the purposes of such a grant as specified; issue awards to research the effects of the current pandemic and potential future pandemics; and provide flexibility on awards to account for facility closures or other limitations during the COVID-19 public health emergency. Agencies must provide the support as rapidly as possible. Provided funds shall remain available through FY2021.