Supreme Court Term Limits and Regular Appointments Act of 2021 This bill establishes staggered, 18-year terms for Supreme Court Justices and limits the Senate's advice and consent authority in relation to the appointment of Justices. Specifically, the bill requires the President to appoint a Supreme Court Justice every two years. If the appointment of a Justice would result in more than nine Justices on the Court, then the nine most junior Justices shall make up the panel of Justices exercising judicial power in cases and controversies. Further, any Justice who has served a total of 18 years is deemed retired from regular service and may continue to serve as a Senior Justice. Senior Justices may continue to perform judicial duties assigned to them by the Chief Justice. However, no Justice appointed before the date of enactment shall be counted towards such panel, nor shall they be required to retire from regular active service. In the event of a vacancy on the Court, the Chief Justice must assign the Justice most recently designated as a Senior Justice to serve on the Court until the appointment of a new Justice. Additionally, the Senate's advice and consent authority is waived if the Senate does not act within 120 days of a Justice's nomination.