Wright joined Salford City’s academy in October 2023 and made a major impact, enjoying a prolific first season as a scholar in which he scored more than 40 goals. He also gained early senior experience, making his first-team bow in the EFL Trophy against Wolves U21s in November 2024, before appearing in the Emirates FA Cup away to Manchester City and twice in League Two while still an Under-18.

Liverpool signed Wright from Salford City in August 2025 and integrated him into their academy system at Kirkby. He moved into the U21 side, where he continued to develop as a central striker despite injury interruptions, contributing four goals and five assists in Premier League 2 during the 2025/26 season. Wright first appeared on a Liverpool first-team teamsheet in the Premier League on 25 April 2026.