No Pensions for Corrupt Politicians Act of 2021 This bill makes a Member of Congress who has been convicted of a crime related to public corruption ineligible to receive certain retirement payments between the date of sentencing and the date of final conviction. Such retirement payments are those made under the Civil Service Retirement System or the Federal Employees' Retirement System based on the individual's service as a Member. Under current law, a Member must forgo receipt of these payments only after a final conviction (i.e., after the exhaustion of all appeals under the judicial process). The bill eliminates these payments to a Member from the date of sentencing for the conviction.