Teaching Engaged Citizenship Act of 2021 This bill provides resources to expand civic education. Specifically, the bill requires the Department of Education (ED) to establish the Civic Education and Service Learning Grant Program to award grants to eligible entities (e.g., state educational agencies) for promoting and expanding civic education in public elementary and secondary schools. Next, the bill creates the Office of Civic Education within ED to promote civic education throughout the United States. The office must establish the Center for Civic Excellence to analyze programs created with the use of grant funds and develop best practices for implementing civic education. Further, the bill establishes the role of Assistant Secretary for Civic Education, whose responsibilities shall include managing the grant program established by the bill. It also establishes an advisory committee to advise the assistant secretary on civic education policy. The bill requires the National Assessment of Educational Progress in civics and history to be administered every two years to certain grade levels. Further, civics and history assessment data must be published in the aggregate for the United States and separately for each state. Additionally, the bill establishes an annual Excellence in Civics Award to highlight excellence in the development and teaching of civic education and service learning. The Library of Congress, the Institute of Museum and Library Services, and the National Archives and Records Administration must work jointly to develop and publicly distribute educational materials and teaching resources related to civic education and effective citizenship.