Strengthening Training and Accessibility for New and Diverse Apprenticeships through Relevant and Dependable Standards Act or the STANDARDS Act This bill provides statutory authority and modifies standards for registered apprenticeships, youth apprenticeships, and pre-apprenticeship programs in the Department of Labor. In addition, the bill also provides statutory authority for (1) the Office of Apprenticeship within Labor to formulate and promote the furtherance of certain quality standards necessary to safeguard the welfare of apprentices, and (2) requirements for apprenticeship agreements between a program sponsor and an apprentice.