On 30 November 2013, Leitch made his debut for Motherwell as a substitute in a surprise 1–0 defeat against Lanarkshire derby opponents Albion Rovers in the Scottish Cup.[1] His first start came on 1 March 2014, in a 4–1 win against Heart of Midlothian.[2] On 4 June 2014, Leitch signed a new two-year contract at Motherwell.[3]
Leitch missed a large part of the 2014–15 season after suffering a cruciate ligament injury in an under-20 match against St Johnstone in October 2014.[4] He was released by the club at the end of the 2015–16 season after his contract expired.[5]
Airdrieonians
On 2 September 2016, Leitch signed for Airdrieonians, joining permanently having already played for the club as a trialist.[6]
Peterhead
Leitch signed a one-year contract with Scottish League Two club Peterhead on 4 August 2017.[7] On 4 May 2019, he scored twice as Peterhead won 2–0 away to Queen's Park at Hampden, a result which clinched the League Two title.[8]