Keep It in the Ground Act of 2021 This bill eliminates new fossil fuel production projects on federal public land and waters. Specifically, it prohibits the Bureau of Ocean Energy Management (BOEM) from issuing, renewing, reinstating, or extending any nonproducing lease, or issuing any authorization for the exploration or production of fossil fuel on the Outer Continental Shelf. BOEM must also cancel any lease issued in the Beaufort Sea, Cook Inlet, or Chukchi Sea (three of the five bodies of water that encompass the Alaska Outer Continental Shelf). Further, the Bureau of Land Management (BLM) may not issue, renew, reinstate, or extend any nonproducing lease for the exploration or production of any onshore fossil fuels on land subject to the Mineral Leasing Act. The bill provides for exceptions if there is an imminent national security threat that would be significantly reduced by granting an exception. In addition, BOEM and the BLM may allow a nonproducing lease to be renewed or extended if (1) the lease contract was signed before enactment of this bill, and (2) it is determined that giving effect to any provision of this bill is likely to lead to a judicial ruling that there was a material breach of the nonproducing lease contract.