Biochar Innovations and Opportunities for Conservation, Health, and Advancements in Research Act of 2021 or the BIOCHAR Act of 2021 This bill establishes two temporary programs to encourage research, development, and commercialization of biochar. This is carbonized biomass produced by converting plant matter through reductive thermal processing for nonfuel uses. First, the Department of Agriculture (USDA) and the Department of Energy (DOE) must fund biochar demonstration projects through state, tribal, or local governments; land-grant colleges or universities; or private, nonprofit, or cooperative entities. In selecting projects, the departments must prioritize, for example, projects that (1) have the greatest potential for carbon sequestration; and (2) create new jobs and economic benefits, particularly in rural areas. Projects may use funds for various activities, including developing commercially and technologically viable biochar production units and demonstrating cost-effective market opportunities for biochar and biochar-based products. At least 50% of the plant matter used in a project must come from forest thinning and management activities on National Forest System land. In addition, USDA and DOE must conduct research related to the biochar produced from the projects. Second, USDA must establish a grant program for land-grant colleges and universities to conduct applied research on environmental and economic benefits of biochar. For the duration of the two programs, USDA and DOE must periodically report to Congress about issues related to commercialization of biochar and the status of the programs. The programs terminate after 10 years.