Layoff Prevention Act of 2021 This bill extends temporary funding to reimburse states for making short-time compensation (STC) payments under existing or new STC programs for weeks of unemployment ending on or before five years and six months after enactment of this bill. (STC, also known as work sharing, is a program that provides prorated unemployment compensation to workers whose hours have been reduced in lieu of a layoff.) Under current law, this reimbursement is available for weeks of unemployment ending on or before September 6, 2021. The bill also extends funding to support STC payments by states that do not have STC programs under state law through 2 years and 13 weeks after enactment of this bill. Under current law, this assistance applies to weeks of unemployment ending on or before September 6, 2021. Finally, the bill increases funding to the Department of Labor for awarding grants to states to (1) implement, or improve administration of, STC programs; or (2) promote, and enroll employers in, STC programs. In addition, the bill modifies the formula used to allocate such grants. Labor may not award a grant with respect to an application submitted after December 31, 2026. Such changes are retroactive to March 27, 2020.