Tim Hart Wildland Firefighter Classification and Pay Parity Act or Tim's Act This bill increases compensation for federal wildland firefighters (including qualifying prevailing rate employees) and establishes related requirements. The bill increases the minimum rate of basic pay for firefighters at General Schedule (GS) levels 1 through 5 to at least the rate of pay for step 3 of GS-6. (A wildland firefighter engages in wildfire management activities, which include aviation, dispatch, and fuels management.) The bill also increases the minimum rate of basic pay for wildland firefighters at GS-6 through 15 by specified percentages, with comparable increases to prevailing rate employees who are wildland firefighters. Next, the bill requires wildland firefighters (including prevailing rate employees) to be paid for sleep and rest periods when deployed to the field on continuous duty status to respond to a qualifying incident at 50% of their hourly rate of basic pay. The bill also mandates a nine-hour sleep and rest period for every 24-hour duty period. The bill also establishes paid leave, a right to buy back service time for retirement credit purposes, and other benefits for wildland firefighters. The bill directs the Office of Workers' Compensation Programs within the Department of Labor to ensure that psychological stress-related injuries and illnesses correlated to fire protection work are compensated and to expedite related claims. Federally-employed firefighters who are not wildland firefighters must also receive pay and benefit increases comparable to the increases provided to wildland firefighters under this bill.