Leveraging Effective Apprenticeships to Rebuild National Skills Act or the LEARNS Act This bill establishes, in the Employment and Training Administration of the Department of Labor, an Office of Apprenticeship to: determine whether an apprenticeship program meets requirements for registration and maintains the standards necessary to remain registered, manage the national apprenticeship system (the collective group of registered apprenticeship programs and pre-apprenticeship programs in the nation), and make grants on a competitive basis to eligible entities to carry out projects that support development of pre-apprenticeship programs. The bill also establishes in Labor a National Advisory Committee on Apprenticeships. Labor and the Department of Education shall establish a voluntary Registered Apprenticeship-College Collaborative consisting of the sponsors carrying out registered apprenticeship programs, two- or four-year postsecondary educational institutions, and organizations that represent such programs or institutions, that agree to meet certain criteria in order to promote stronger connections between the registered apprenticeship programs involved and participating two- and four-year postsecondary educational institutions. Labor shall make assistance payments to eligible sponsors of new registered apprenticeship programs or of existing programs that add employers as new partners, that may include joint labor-management registered apprenticeship programs.