Leverage Prior Skills Act - Amends the Workforce Investment Act of 1998 to require a governor, in establishing a procedure for local workforce investment boards in the state in determining the initial eligibility of a provider to receive funds for a program of training services, to require the applicant proposing a program that leads to a recognized postsecondary credential to include in the application information on the quality of the services that lead to that credential.

Requires a state to use federal funds reserved to carry out statewide employment and training activities (other than certain statewide rapid response activities) to identify and implement a process by which local boards will contract with providers of training services, or identify eligible providers of training services, only if the providers involved agree to:

• use direct assessments to assess the prior learning of the participants in noncredit employment and training programs; and
• take that prior learning into account when determining whether a participant has earned credit hours or made progress toward earning a degree from an institution of higher education, or has earned or made progress towards earning a recognized postsecondary credential.