Moore was born in Walthamstow in East London, but moved to France as a seven-year-old. Moore spent a year in the academy of his local side West Ham United before moving to France. Upon arriving in France, he joined amateur club Etaples before joining the academy at RC Lens at the age of 12.
Lens
Having made a progression through the RC Lens' academy, Moore signed his first professional contract with the club on 8 December2014. On 3 May 2015, with Antoine Kombouaré as coach, he made his first-team debut for Lens, starting in an away derby match against Lilleplaying out of position at right back and producing an assist for his team's only goal in a 3–1 loss. Moore went on to make four appearance in the 2014–15 season. In the 2015–16 season, Moore made five appearance for the club. However, his first team opportunities were limited after he fell out of favour with manager Kombouaré and was sent to play in the reserves. Despite this, Moore was the subject of a €10 million transfer bid from Lyon in the January transfer window. RC Lens rejected the bid, demanding €15 million instead. Moore was expected to leave the club by the end of the January transfer window, but no club made an offer and he stayed at the club for the rest of the season. Ahead of the 2016–17 season, Moore's future at RC Lens became uncertain and he found himself linked with a move back to England, with Bristol City, Tottenham Hotspur, Southampton, West Ham United and Crystal Palace also showed an interest in signing him. Amid the transfer speculation, Moore was expected to fight for a first team place under the new management of Alain Casanova.
Bristol City
On 25 August 2016, Moore signed for Championship club Bristol City on a three-year contract for an undisclosed fee believed to be in the region of £1.5m. Upon joining the club, Moore revealed that then-teammate Tammy Abraham played a role in convincing him to join Bristol City. He made his debut in an EFL Cup match away to Fulham, in which Bristol City won 2–1. Less than a week after the January transfer window opened in 2017, Moore was loaned out to struggling League One side Bury to gain further experience. On 30 August 2017, Moore signed for Cheltenham Townon loan until January 2018.
