Coal Royalty Fairness and Communities Investment Act of 2021 This bill addresses coal royalties and the economic vitality of coal communities, including by (1) requiring the coal lease royalty to be at least 12.5% of the assessment value of federal coal (currently, 12.5% of the value as defined by regulation); (2) establishing the Coal Area Economic Revitalization Fund; (3) providing grant assistance to impacted communities for economic and workforce development programs; (4) providing financial assistance for the design, construction, and operation of large-scale projects to capture and store carbon dioxide emissions from industrial sources; and (5) providing technical assistance and educational outreach to impacted communities.