Born in
Keighley, West Yorkshire, In August 2005, he and fellow Bradford City player
Danny Forrest moved to
Conference National club
Halifax Town on
loan—Wright's an initial one-month loan deal. It would be his only senior appearance for Bradford. before playing a further 36 games the following season. During the campaign, he picked up his first red card of his career, in a 1–0 defeat to
Aldershot Town. Wright made 26 appearances during his loan spell at the
Kassam Stadium. He was appointed club captain in July 2011 and extended his contract by a year in October 2011. After six seasons, and having made 278 appearances and captained the squad to second place in League Two and promotion in the
2015–16 season, Wright – the club's longest-serving player – left Oxford by mutual consent on 9 July 2016. Later that day, he signed for League One club
Sheffield United on a two-year contract. This was the club's first win of what became a promotion-winning season. Wright made 30 appearances in his first season as a Blade and remained unbeaten throughout the whole campaign, entering the record books in the process. In the 2017–18 season Wright made 17 appearances for Sheffield United in the
EFL Championship. This was the highest level Wright played at in his career (although he remained a Sheffield United player until part way through the club's 2019–20 season in the
Premier League, he made no appearances). On 2 September 2019, Wright joined
EFL League One side
Bolton Wanderers on loan until January and was one of nine players Bolton signed on deadline day. He made his debut on 14 September, starting against
Rotherham United in a 6–1 defeat. His contract with Sheffield United was terminated by mutual consent on 31 January 2020. He signed for
Hereford on 18 September 2020. On 14 November 2020, Wright was released by
Hereford. On 26 February 2021, Wright joined
League Two side
Mansfield Town on a contract until the end of May 2021. On 22 July 2021, Wright signed for Conference North side
Boston United. Wright was released at the end of the
2021–22 season. In June 2022, Wright joined
Northern Premier League Division One East club
Grantham Town, being named captain for the
2022–23 season. In July 2023, Wright joined
United Counties League Premier Division North club
Sherwood Colliery. Having helped the club to promotion, he joined
Eastwood in July 2024. ==Style of play==