Growing Education Achievement Training Academies for Teachers and Principals Act or the GREAT Teachers and Principals Act - Authorizes the Secretary of Education to award grants to states to: (1) create or approve teacher or principal preparation academies and create or designate authorizers of those academies; (2) support the creation and operation of such academies; and (3) award subgrants to nonprofit entities to establish or expand such academies, measure their effectiveness, or recruit enrollees who have demonstrated strong potential to be effective teachers or principals.

Requires each academy to enter into a charter with an authorizer that specifies the goals and outcomes expected of the academy and the obligations of the authorizer. Prohibits authorizers from renewing an academy's charter if it fails to produce the minimum number or percentage of effective teachers or principals specified in its charter.

Requires each academy to provide: (1) enrollees with a significant portion of their training through clinical preparation that partners them with successful teacher or principal mentors, and (2) certificates of completion only to graduates who demonstrate a track record of success in preparing students for college and careers.

Requires state grantees to recognize a certificate of completion from an academy as at least the equivalent of a master's degree in education for the purposes of teacher or principal hiring, retention, compensation, and promotion in the state.

Directs the Secretary to enter into an interagency agreement with the Corporation for National and Community Service under which the Corporation approves national service positions for candidates at each teacher or principal preparation academy receiving financial assistance under this Act.