Born in Grafton, NSW, Carly Leeson represented New South Wales at under-15 and under-18 level and was a member of the Shooting Stars squad that toured Sri Lanka in 2015.
Leeson signed with the Sydney Sixers ahead of WBBL|02 in 2016–17, debuting against the Melbourne Renegades.
She spent three seasons with the club before moving to the Renegades ahead of WBBL|05, where she remained until her contract was not renewed at the end of WBBL|08. Her next WBBL appearance came two years later, when she was signed on a one-year deal by the Perth Scorchers ahead of WBBL|10.
In the WNCL, Leeson signed a contract with the NSW Breakers ahead of the 2017–18 season, but had to wait until 2019 to make her debut.
She made the move to Canberra ahead of 2019-20 after signing a contract with the ACT Meteors.