21st Century Civilian Conservation and Climate Corps Act This bill temporarily authorizes and provides funding for the President to establish and operate a Civilian Conservation and Climate Corps to employ young adults (ages 16-25) in connection with public conservation and climate projects. If available funds are insufficient to employ every eligible individual seeking employment with the corps, preference must be given, in order, to (1) unemployed veterans, (2) unemployed individuals who have exhausted their unemployment benefits, (3) individuals who are otherwise eligible for unemployment benefits, (4) members of groups determined to have suffered economic or social disadvantages to finding decent work, and (5) other unemployed individuals. The corps must pay employees wages comparable to wages paid to public-sector employees. The corps may also provide room, board, and clothing for employees, but the cost of these accommodations must be deducted from wages.