A graduate of the Academy at Crewe Alexandra, he played on loan for Halifax Town, Newcastle Town, ÍBV (Iceland), and Curzon Ashton. He spent six years with Crewe, winning the League Two play-offs in 2012 and the Football League Trophy in 2013. He signed with Yeovil Town in June 2014, but moved on to Port Vale in July 2015 after a poor season with Yeovil. He finished as Port Vale's top-scorer, before moving on to Shrewsbury Town in June 2016. He joined Scottish Premiership club Dundee on loan in August 2017.
Whilst on the books at Crewe Alexandra as a youth player, Leitch-Smith was loaned out to non-League clubs Halifax Town in November 2008 and Newcastle Town in March 2009. He signed his first professional contract in April 2009, before joining Icelandic club ÍBV on loan. He was recalled from his loan, along with Chris Clements, in early September due to injury problems at Crewe.
He made his League Two debut for Crewe at Gresty Road in a 3–2 defeat to Bury on 29 September 2009, replacing Joel Grant as a substitute in the 80th minute. This was his only appearance of the 2009–10 season. He joined Curzon Ashton on loan in March 2010. He scored seven goals in ten Northern Premier League appearances, which was enough to win him a new contract at Crewe.
He scored his first goal in the Football League on 21 August 2010, adding the final goal of the "Railwaymen's" 7–0 win over Barnet. However, he was limited to only 18 appearances in the 2010–11 season as he struggled to step up to first team football, and manager Dario Gradi devised a special pre-season fitness programme in the summer to help him to adapt to senior football.
Leitch-Smith scored nine goals in 44 games in the 2011–12 campaign. He signed a new one-year contract in April 2012, and manager Steve Davis stated "I'd like to think that he can become the 15 to 20 goal a season man we need." On 27 May, he played the first 85 minutes of the League Two play-off Final victory over Cheltenham Town at Wembley Stadium, providing the assist for Byron Moore's goal which secured the 2–0 victory and Crewe's promotion into League One.
He scored six goals in 35 matches in the 2012–13 season. On 7 April he made another appearance at Wembley, as the Alex beat Southend United 2–0 in the Football League Trophy Final; he was an 83rd-minute substitute for Max Clayton. The next month he signed a one-year extension to his existing contract. However, he played just 24 games in the 2013–14 season, scoring two goals. He left Crewe after an eleven-year association with his hometown club, saying he felt like a "part of the furniture" of the club.
In June 2014, Leitch-Smith signed for Gary Johnson's League One club Yeovil Town on a two-year contract. He struggled in his first season for the "Glovers", as he was played mostly in a wide position. He only scored twice in 38 appearances and was one of four players offered a contract termination by new manager Paul Sturrock following Yeovil's relegation into League Two at the end of the season.
In July 2015, Leitch-Smith signed a 12-month deal with League One side Port Vale after agreeing to leave Yeovil. He earned the contract after impressing manager Rob Page during pre-season training. He scored his first goal for the "Valiants" on 14 November, with a header than opened the scoring in a 2–1 win at Barnsley. This was the start a sequence of five goals in four games, which was the best scoring run of his career to that point. For his performances he was short-listed for the League One player of the month award. After scoring his sixth goal of the season in a 1–1 draw with Scunthorpe United at Vale Park on 12 December he was named the Football League Paper's team of the day. He scored four goals in four games in January to go into double figures for the season and earn himself a nomination for the PFA fans' player of the month award for League One. Chairman Norman Smurthwaite confirmed that Leitch-Smith had rejected the offer of a new contract from the club in May 2016.
Leitch-Smith signed with League One side Shrewsbury Town in June 2016, along with former Port Vale teammates Ryan McGivern and Louis Dodds. He scored his first goal for the club in the first minute of a first-round League Cup tie against Championship side Huddersfield Town, with Shrewsbury going on to win 2–1. After an indifferent run of form in Micky Mellon's last weeks as manager, he was recalled to the starting eleven by new manager Paul Hurst for an FA Cup first round tie on 5 November, and scored the second goal in a 3–0 victory over Barnet. He was limited to five goals in 12 starts and nine substitute appearances throughout the 2016–17 campaign, and was not allocated a squad number ahead of the following season as he was not in the club's future plans.
On 31 August 2017, he joined Scottish Premiership club Dundee on a five-month loan deal. He his debut for the "Dee" on 9 September, coming on as a 38th-minute substitute for Scott Allan in a 4–1 defeat at Rangers. He was given his first start at Dens Park seven days later, scoring twice in a 3–2 win over St Johnstone.
Though Leitch-Smith lacks natural athleticism and pace, he is an intelligent and creative attacker with good technical skills and a high work rate. Former teammate Tom Pope stated that Leitch-Smith was "one of the most intelligent strikers... in League One".As of match played 16 September 2017.
with Crewe Alexandra
Football League Two play-off winner: 2012
Football League Trophy winner: 2013