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 December 31, 2020: (1) the TAA program, and (2) the reemployment trade adjustment assistance (RTAA) program.

Makes funds available through FY2020, and for the period beginning October 1-December 31, 2020 (first quarter of FY2021), for training of adversely affected workers, employment and case management services, and job search expenses and relocation expenses.

Reauthorizes appropriations: (1) through December 31, 2020, for the TAA program for workers; and (2) through FY2020, and for the first quarter of FY2021, for the TAA program for firms, communities, and farmers.

Prescribes TAA eligibility requirements for adversely affected workers in public agencies.

Revises trade readjustment allowance (TRA) program requirements.

Increases from 65 to 78 additional weeks of TRA payments in a 91-week period the length of additional time permissible to complete training.

Repeals the authority of a state to use funds for employment and case management services and relocation allowances to allow an adversely affected worker who is certified to file an application for a job search allowance and relocation allowance. (Continues to authorize adversely affected workers to apply for the job search allowance as well as the relocation allowance.)

Increases from $1,250 to $1,500 the maximum job search allowance and maximum relocation allowance that may be granted to an adversely affected worker.

Revises the reemployment trade adjustment assistance (RTAA) program.

Increases from: (1) $50,000 to $55,000 the maximum amount an RTAA-eligible worker may earn in wages from reemployment, and (2) $10,000 to $12,000 the maximum payment of RTAA (or wage subsidy) to an eligible older worker.

Specifies criteria the Secretary 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 Secretary 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.

Amends the Internal Revenue Code to extend through calendar 2021, and increase from 72.5% to 80%, the tax credit for the health insurance coverage costs of Pension Benefit Guaranty Corporation (PBGC) pension and TAA recipients and their dependents.

Amends the Internal Revenue Code, the Employee Retirement Income Security Act of 1974, and the Public Health Service Act to extend through December 31, 2020, the TAA pre-certification period rule disregarding, for a specified period, any 63-day lapse in creditable health care coverage for TAA workers.

Extends also through December 31, 2020, the continued eligibility of certain qualified TAA-eligible individuals and PBGC pension recipients for COBRA premium assistance.