Afghanistan Counterterrorism, Oversight, and Accountability Act of 2021 This bill imposes sanctions involving Afghanistan and addresses related issues. The President must impose, with certain exceptions, visa- and property-blocking sanctions on any foreign individual or entity that (1) provides support to any terrorist group in Afghanistan, (2) is responsible for or complicit in serious human rights abuses in Afghanistan, or (3) plays a significant role in international narcotics trafficking centered in Afghanistan. The President may also impose such sanctions on any foreign individual or entity that provides certain support for (1) the Taliban or any Taliban member, or (2) any agency of the Taliban-controlled government of Afghanistan. Additionally, the Department of State must (1) require U.S. representatives to the United Nations to advocate and vote to maintain sanctions against the Taliban, and (2) encourage allies and partner countries to impose sanctions against the Taliban. The State Department may suspend the sanctions imposed under this bill upon certifying to Congress that the Taliban has taken certain actions, such as breaking all ties with other terrorist groups. The State Department must establish a task force to (1) implement a strategy relating to the evacuation of Afghanistan, and (2) identify individuals in Afghanistan who have sought admission into the United States as a refugee or humanitarian parolee. The bill requires various reports, including on (1) a revised strategy for engagement with South and Central Asian countries after the U.S. withdrawal from Afghanistan, (2) a counterterrorism strategy for Afghanistan, and (3) the extent of Taliban human rights abuses.