Veterans Burn Pits Exposure Recognition Act of 2021 This bill requires the Department of Veterans Affairs (VA) to concede, for the purposes of health care benefits and wartime disability compensation, that a veteran was exposed to certain toxic substances, chemicals, and hazards from burn pits if such veteran served on active duty in a covered location during a specified time frame (unless there is affirmative evidence to establish that the veteran was not exposed during such service). A burn pit is an area used for burning solid waste in open air without equipment. Specifically, the bill covers the following locations and corresponding time periods: Iraq between August 2, 1990, and February 28, 1991, as well as from March 19, 2003, until burn pits are no longer used in this location; Somalia and Southwest Asia (including Kuwait, Saudi Arabia, Oman, and Qatar) from August 2, 1990, until burn pits are no longer used in these locations; and Afghanistan, Syria, Jordan, Egypt, Lebanon, Yemen, Uzbekistan, the Philippines, and Djibouti from September 11, 2001, until burn pits are no longer used in these locations. Under the bill, if an exposed veteran submits insufficient evidence to establish a service-connection for purposes of disability compensation, the VA shall provide a medical examination and request a medical opinion regarding a causal link between the disability and a toxin, chemical, or hazard.