After playing for Tranmere Rovers, Everton and Blackburn Rovers in youth football, Wright made the switch to King Power Stadium in February 2018. After delivering a string of positive performances for the Club's Development Squad, a loan move was soon on the card for Wright.
The 2020/21 season would end with the Sky Bet League 2 for Wright and his Cheltenham Town team-mates, as the City youngster made 17 outings, scoring four goals. He also spent last term with the Robins in the third tier, netting another nine strikes in 28 appearances.