Strengthening Youth Apprenticeships Act of 2023 This bill requires (1) the Department of Labor to enter into an agreement with the Department of Education to promote the integration and alignment of apprenticeship programs with secondary, postsecondary, and adult education; and (2) Labor to award grants to eligible entities (e.g., partnerships that include state or local educational agencies, community colleges, and community-based organizations) to create or expand youth apprenticeship programs.