A product of West Bromwich Albion's academy, Wright was loaned out to Kidderminster Harriers for the first half of the 2015–16 season in order to gain experience of senior football.
[6] After featuring for West Brom's Under-23 side against Millwall in the EFL Trophy in August 2016, Wright was loaned out to Coventry City until 9 January 2017.
[10] On 1 September 2017, after numerous trials with Football League sides, Wright opted to return to Kidderminster Harriers on a one-year deal.
Wright scored 4 goals in a single game for Bohs as they defeated fellow Dublin club UCD in August 2019.
On 17 August 2021, it was announced that Wright had returned to the League of Ireland, signing for Sligo Rovers for the final 4 months of the season.