Learning Recovery Act of 2021 This bill establishes a program through which the Department of Education must award grants to state educational agencies and, through them, allocations to local educational agencies (LEAs) to provide students with additional learning time and related services. It also directs the Institute of Education Sciences (IES) to study and report on learning recovery. Specifically, LEAs must use funds to implement attendance-intervention strategies that reengage students and their families, support salaries and benefits for teachers and staff, and carry out school extension programs. School extension program refers to an evidence-based program (e.g., summer-school, extended-day, or extended-school-year program) at an elementary or secondary school that provides students with additional learning time. Further, LEAs may use funds for certain activities such as providing students with mental health services, reestablishing after-school programs, and supporting existing activities to combat learning loss due to the COVID-19 (i.e., coronavirus disease 2019) pandemic. The IES must, within 30 days, begin to study interventions and strategies to address learning recovery for all students, including students with disabilities, minority children, English learners, and low-income students. Further, the IES must disseminate findings to educational agencies.