Trade Adjustment Assistance Enhancement Act of 2015 Amends the Trade Adjustment Assistance Extension Act of 2011 to repeal the declaration that trade adjustment assistance (TAA) program requirements in effect as of February 13, 2011, under the Trade Act of 1974 shall apply to petitions for certification to apply for TAA for workers, firms, and farmers that are filed before January 1, 2014. Amends the Trade Act of 1974 to extend through June 30, 2021: the TAA program, and the reemployment trade adjustment assistance (RTAA) program. Makes funds available for FY2015-FY2021 for training of adversely affected workers as well as (through June 30, 2021) reemployment and case management services. Reauthorizes appropriations: through June 30, 2021, for the TAA program for workers; and for FY2015-FY2021 for the TAA program for firms and farmers. Revises and replaces core indicators of performance with primary indicators of performance. Adds among other factors the percentage and number of workers receiving TAA benefits who are in: unsubsidized employment, and an education or training program that leads to a recognized postsecondary schooling credential or employment and who are achieving measurable gains in skills toward that credential or employment. Specifies criteria the Department of Labor must use to determine the eligibility of workers to apply for TAA if no determination has been made, upon enactment of this Act, as to whether to certify a group of workers or firms as eligible pursuant to a petition filed between January 1, 2014, and enactment of this Act. Requires the Department to reconsider any determination made before enactment of this Act not to certify such workers or firms, and to certify them as eligible if they meet the specified requirements. Increases from 52 to 65 additional weeks of TAA payments in a 78-week period the length of additional time permissible to complete training.