First Step Implementation Act of 2021 This bill makes various changes related to federal sentencing law and requires the Department of Justice (DOJ) to establish procedures to ensure the prompt release and accuracy of employment-related background check records. The bill allows certain reduced mandatory minimum sentences for drug offenses to be applied retroactively to offenders who committed their offenses on or before December 21, 2018; permits a court, in certain circumstances, to grant safety valve relief (i.e., impose a sentence without regard to the statutory mandatory minimum penalty for certain drug offenses) for an otherwise eligible defendant who does not meet the requirement pertaining to criminal history; permits a court to reduce a sentence imposed on a defendant convicted as an adult for an offense committed as a juvenile if the defendant has served at least 20 years of the sentence; establishes a process to seal and expunge certain records of juvenile nonviolent offenses; and requires DOJ to establish and enforce procedures to ensure that records exchanged for employment-related background checks are promptly released and accurate.