Spotted playing for non-league Farnborough, he joined Brentford in August 2009 following a successful trial period, and went on to make his debut against Hartlepool United the following May.
His breakthrough campaign came in 2012/13 when he helped the Bees to the League One Play-Off final against Yeovil Town and a draw against European champions Chelsea in the FA Cup.
Given his impressive form, he was signed by newly-promoted Premier League side Cardiff City that summer on a four-year deal and was loaned out to Bristol City later that season.
With the Bluebirds relegated back to the Championship, Moore made his league debut for the club against Fulham in January 2015 and enjoyed a regular run of games under boss Russell Slade.
In August 2016 he joined League One Sheffield United, and in his first season was named in the PFA Team of the Year as the Blades won promotion to the Championship.
He has since made over 60 league appearances for the club, including a Premier League bow against Manchester United in November 2019.