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. The early release pilot program 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, expands eligibility to offenders who have served at least one-half (currently, two-thirds) of their prison term, 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 and shortens the waiting period for judicial review during the COVID-19 pandemic. Second, the bill modifies the compassionate release process. The compassionate release process 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, specifies that vulnerability to COVID-19 is a basis for compassionate release, and shortens the waiting period for judicial review during the COVID-19 pandemic.