Time to Rescue United States Trusts Act of 2021 or the TRUST Act of 2021 This bill establishes congressional rescue committees to develop recommendations and legislation to improve critical social contract programs. A critical social contract program is a federal program for which a federal trust fund is established (e.g., Social Security, Medicare, and federal highway programs), with outlays of at least $20 billion during the year preceding the year in which this bill is enacted, and for which the amount of dedicated federal funds and federal trust fund balances will be inadequate to meet the total amount of outlays of the program that would otherwise be made. Each rescue committee may develop recommendations and legislation to improve the program for which it was established, including by (1) increasing the duration of positive balances of the federal trust fund established for the program, and (2) providing for the solvency of the federal trust fund established for the program during a 75-year period. Congress must use specified expedited legislative procedures to consider legislation that is approved and submitted by the rescue committees.