[1][2] After securing a scholarship, Cartwright relocated to Brisbane in 2014 to attend private Lutheran school St Peters College.

[3] He competed in the men's 100 metre freestyle event at the 2017 World Aquatics Championships.

[4][5] At the 2018 Commonwealth Games on the Gold Coast, Cartwright won two gold medals as part of the teams who won the 4x100m freestyle relay and the 4x100m medley relay.

[2][6] Cartwright was part of the winning 4 x 100 metre relay and the 4 x 100 metre freestyle teams at the 2022 and 2023 World Aquatics Championships in Budapest and Fukushima respectively, winning a collective total of three gold medals and one silver medal.

[7][8] Following this success, Cartwright won another silver medal at the 2024 World Aquatics Championships in Doha as part of the mixed 4 x 100 metre freestyle relay team.