Noncontiguous Shipping Relief Act of 2021 This bill revises coastwise laws, commonly known as the Jones Act, that govern domestic transportation of merchandise or passengers by vessels. The Jones Act requires that vessels transporting merchandise or passengers between Puerto Rico and other U.S. ports be built in the United States, be at least 75% owned by U.S. citizens, and be mostly crewed by U.S. citizens. The bill exempts foreign-flag vessels transporting merchandise on a route in noncontiguous trade from Jones Act requirements. The bill sets forth other requirements, including (1) labor standards, (2) minimum requirements for vessels engaging in the transportation of cargo or merchandise in domestic coastwise trade, (3) environmental standards, and (4) requirements for certain non-citizens that irregularly engage in domestic coastwise trade.