Wright began his youth career with the LA Galaxy Academy in 2011, before moving to the New York Cosmos in 2014. He made his professional debut with Schalke 04 in the German Bundesliga in 2016, before going on loan to Sandhausen in the 2. Bundesliga. In 2019, Wright signed with Dutch club VVV-Venlo, where he enjoyed a successful spell before joining Coventry City in 2021.