Leveraging and Energizing America's Apprenticeship Programs Act or the LEAP Act This bill amends the Internal Revenue Code to allow employers a business-related tax credit of $1,500 for hiring an apprenticeship employee who has not attained age 25 at the close of the taxable year or $1,000 for hiring an apprenticeship employee who has attained age 25. The credit is available for no more than two taxable years with respect to any apprenticeship employee. An "apprenticeship employee" means any employee who is: (1) a party to an apprenticeship agreement registered with the Office of Apprenticeship of the Employment and Training Administration of the Department of Labor or a recognized state apprenticeship agency; and (2) employed by the employer in the occupation identified in the apprenticeship agreement, whether or not the employer is a party to such agreement.