Apprenticeship Program Clearinghouse Act This bill requires the Department of Labor to enter into an interagency agreement with the Department of Education (ED) to promote and support integration and alignment of programs under the national apprenticeship system with secondary, postsecondary, and adult education. The agreement must require that Labor and ED disseminate information on the value of programs under the national apprenticeship system and require the creation of a clearinghouse of best practices for improving performance and increasing alignment of education and programs under the national apprenticeship system, including career pathways.