Born in Exeter, Moore-Taylor started his footballing career at Stoke Hill AFC before signing his first professional contract with Exeter City in summer 2012 after progressing through the club's youth academy.[3]
On 19 June 2018, Moore-Taylor followed former Exeter manager Paul Tisdale to Milton Keynes Dons after six years at Exeter, signing a two-year deal after he activated a clause in his contract to leave Exeter.[5] He scored his first goal for the club on 12 January 2019 during a 4–3 away defeat to Bury.[6] A knee injury suffered two weeks later in a 1–0 away defeat to Grimsby Town resulted in him being sidelined for the remainder of the campaign.[7] Following the conclusion of the 2019–20 season, Moore-Taylor was one of nine players released by the club.[8]