Born in Sandown on the Isle of Wight, Moore started at Brading Town. He was signed by Premier League side Southampton academy. Moore revealed he was released by the club for being too small. He returned to Isle of Wight based side Brading Town, before signing for Farnborough.
Moore signed with Brentford in August 2009 after spending the summer at the club on trial, but had to wait until May 2010 to make his debut, when he appeared against Hartlepool United as a substitute for regular number one goalkeeper Wojciech Szczęsny.
He was loaned out in October 2010 to Basingstoke Town and played until January 2011, in 10 games for the club.
The 2012–13 season was Moore's breakthrough season at Brentford. He started the season as an understudy to goalkeeper Richard Lee. During Lee's time out injured Moore put in some good performances and cemented his place in the Brentford team under Uwe Rösler. He helped Brentford reach the FA Cup fourth round, this included a 2–2 draw with European Champions Chelsea, and finish third in the league missing out on promotion on the final day of the season after a dramatic game with Doncaster Rovers. Brentford entered the play-offs, where they were drawn in the semi-final against Swindon Town. Brentford reached the playoff final defeating Swindon in the semi-finals on penalties (Moore saved Miles Storeys' spotkick in the shootout), but they lost the final to Yeovil Town 2–1.
On 29 July 2013, Moore was signed by Malky Mackay a four-year deal with newly promoted Premier League side Cardiff City. After failing to displace David Marshall, Moore was sent out on loan to Bristol City on 30 January 2014, not long after new manager Ole Gunnar Solskjær took charge of Cardiff. He was sent out on loan to get a regular run of games. Whilst out on loan to Bristol City, Cardiff were relegated from the Premier League.