National Security Powers Act of 2021 This bill limits presidential authorities related to, and increases congressional oversight of, introducing U.S. armed forces into hostilities, arms transactions, and national emergencies. The bill limits presidential authority to introduce U.S. forces into hostilities absent a declaration of war, specific statutory authorization, or when necessary to repel a sudden attack (or imminent threat of an attack). It also establishes procedures for the President to notify Congress of and obtain authorization for the introduction of U.S. forces into hostilities (or the risk of them). Additionally, the bill repeals laws authorizing the use of force abroad and the War Powers Resolution, which provides procedures for Congress and the President to participate in decisions to send U.S. forces into hostilities. For a treaty or other international obligation to authorize the introduction or retention of U.S. forces, Congress must specifically enact implementing legislation to that effect. The President must seek congressional approval before entering, renewing, or extending an arms sale or related transaction if the transaction exceeds specified dollar thresholds. This does not apply to transactions with NATO and its member countries, Australia, Japan, South Korea, Israel, New Zealand, or Taiwan. The bill restricts presidential authorities related to national emergencies, including by limiting the period of a declared emergency to 30 days unless Congress authorizes an extension. The bill also establishes procedures for approving or disapproving an extension, requires the President to provide more detailed reports to Congress about national emergencies, and sets out specific provisions for terminating an emergency.