National Heritage Area Act of 2021 This bill establishes a National Heritage Areas System to recognize certain areas of the United States that tell nationally significant stories and to conserve, enhance, and interpret the areas' natural, historic, scenic, and cultural resources that illustrate significant aspects of U.S. heritage, and authorizes appropriations through FY2034 for each National Heritage Area. Through such system, the Department of the Interior may provide technical and financial assistance to local coordinating entities to support the establishment, development, and continuity of such areas. The bill extends the authority for the Erie Canalway National Heritage Corridor Commission and the Gullah/Geechee Cultural Heritage Corridor Commission until September 30, 2034. The local coordinating entity of a National Heritage Area, not later than three years after the area is included in the National Heritage Area System, shall submit to Interior a management plan for approval. Interior, not later than one year before the authorization for federal funding expires for a National Heritage Area, shall (1) conduct an evaluation of the accomplishments of that area, and (2) submit a report detailing the evaluation to specified congressional committees. Based upon the evaluation, Interior shall prepare a report with recommendations for the National Park Service's continued role, if any, with respect to the area. Interior may carry out or certify a study to assess the suitability and feasibility of designating a specific geographic area as a National Heritage Area to be included in the National Heritage Area System.