Success for Rural Students and Communities Act of 2021 This bill establishes a grant program through which the Department of Education may award funds to eligible partnerships to support rural postsecondary education and economic growth and development in rural communities. A grant recipient must be a partnership whose members represent at least three designated types of organizations, specifically (1) a local educational agency or educational service agency serving a rural area, (2) an institution of higher education (IHE), (3) a regional economic development entity, or (4) a rural community-serving organization with demonstrated success supporting rural students in accessing higher education and attaining degrees. A grant recipient must use awarded funds to carry out no fewer than two specified activities, namely (1) improving postsecondary enrollment rates for rural secondary school students, (2) increasing enrollment and completion rates of rural nontraditional students in degree programs at IHEs, (3) creating or strengthening academic programs at rural-serving IHEs to prepare graduates to enter into high-need occupations in the regional and local economies, or (4) generating local and regional economic development that creates employment opportunities for rural students with postsecondary degrees.