COVID-19 National Service Response Act This bill modifies the Corporation for National and Community Service program to respond to the COVID-19 (i.e., coronavirus disease 2019) national emergency. The corporation shall allow an individual serving in a position eligible for an educational award, who is performing limited service or whose position has been suspended or placed on hold due to COVID-19, to accrue other service hours that will count toward the number of hours needed for the individual's education award. The bill (1) deems certain individuals who are required to exit such positions early at the direction of the corporation to have met the requirements of the position, and (2) makes certain funds available for FY2021 for the program. The corporation may (1) permit fixed-amount grant recipients to maintain a pro rata amount of grant funds at the corporation's discretion for participants who exited, were suspended, or are serving in a limited capacity due to COVID-19; and (2) extend the term of service or waive any upper age limit for national service programs carried out by the National Civilian Community Corps for purposes of addressing disruptions, and minimizing the difficulty in returning to full operation, due to COVID-19.