Wright began his senior rugby career with Easts Tigers, playing Queensland Premier Rugby in 2016.[5] He was selected in the Australian Under-20 team in 2016 and 2017 for the World Championships in Italy and Georgia.[6] Wright joined the Queensland Country team and made his debut in Australia's National Rugby Championship (NRC) in October 2016, playing against the NSW Country Eagles.[7]
In 2017, he signed a two-year professional contract with the Queensland Reds for the following two seasons.[8] After impressing national selectors during the NRC in 2017, Wright played for Australia against the Barbarians in Sydney,[9] and was then chosen as one of two development players in the Wallabies tour squad for the 2017 end-of-year rugby union internationals.[10][11]
Wright made his Super Rugby debut for the Reds off the bench in the team's first match of the 2018 season, playing against the Rebels in Melbourne.[12]
He was selected in the Australia squad for the Bledisloe Cup in 2019,[13] and made his test debut against New Zealand at Eden Park in August that year.[3]
After suffering a run of injuries, Wright returned to the Wallabies fold under newly-appointed coach Joe Schmidt in July 2024. He was made captain for their first test against Wales on their three-test tour of Australia.[3][4]
In October 2025, after eight years at the Queensland Reds, Wright departed the club after a breakdown on contractual agreement terms.[14][15] Wright had played just 58 minutes of rugby in 2025 after sustaining a shoulder injury against Wales on their 2024 tour of Australia.[15]