Continuity for Operators with Necessary Training Required for ATC Contract Towers Act of 2019 or the CONTRACT Act of 2019 This bill exempts certain air traffic controllers from a required reduction in their retirement annuity payment on account of earnings from certain work performed while entitled to such annuity. Under current law, retired Federal Aviation Administration air traffic controllers receive an annuity payment during the period between the mandatory retirement age of 56 and the social security minimum age of 62. Such annuity payment is required to be reduced by a certain percentage of any excess earnings during this period. The bill exempts from such reduction in annuity payments an air traffic controller who participates in the Air Traffic Control Contract Program (a public-private partnership for air traffic control services) following mandatory retirement.