COVID-19 Safer Detention Act of 2021 This bill expands statutory authority for federal prisoners to be released before completing their sentences or to be placed in the community to serve the final portion of their sentences. First, the bill makes changes to the early release pilot program which authorizes the Bureau of Prisons to release early and place on home confinement elderly offenders and terminally ill offenders who meet eligibility criteria. This bill expands eligibility to offenders serving time for an offense under the laws of the District of Columbia, reduces the amount of time an offender must serve by the good time credits earned by the offender, and creates a judicial review process for prisoners. Second, the bill modifies the compassionate release process which authorizes federal courts to reduce a prisoner's sentence and impose a term of probation or supervised released in certain circumstances. This bill expands eligibility to prisoners sentenced before November 1, 1987; and specifies that vulnerability to COVID-19 is a basis for compassionate release. Regarding the judicial review of these release authorities, the bill also (1) authorizes federal courts to appoint counsel to assist defendants, (2) applies statutory rights for crime victims to these proceedings, and (3) shortens the waiting period during the COVID-19 pandemic. Additionally, the bill requires the Government Accountability Office to study postrelease, probation, and pretrial services, including recent changes. Finally, the bill directs the Administrative Office of the U.S. Courts to request resources to address staffing needs in each judicial district, including resources that may be necessary as a result of this bill.