Reilly arrived through the youth ranks of Dumfries club Queen of the South, signing a professional contract before the start of the 2010–11 season. Reilly made his competitive first-team debut on 31 July 2010 in a 5–1 Scottish League Cup first round win versus Dumbarton as an 83rd-minute substitute for Derek Holmes. Reilly marked the occasion by scoring the team's fifth and final goal of the match. Reilly's league debut was as an 86th minute substitute in the season's opening 1–0 away defeat away to Dundee. Reilly scored 15 goals in 22 starts during the 2012–13 season and then scored 12 goals in 19 league starts in the 2013–14 season. In August 2014 Reilly went on trial with English Championship club Brentford.
Heart of Midlothian
On 23 June 2015, it was announced that Reilly had signed a three-year contract with Scottish Premiership club Heart of Midlothian, with an undisclosed development fee being paid to Queen of the South. The announcement stated that Reilly had scored 44 first team goals in over 140 games, including over 80 starting appearances since his debut as a 17-year-old. Reilly scored his first goal for Hearts on 12 August 2015 in a 2–0 win versus Motherwell from the penalty spot. In June 2016, Reilly joined Scottish Championship club Dunfermline Athletic in Fife on a year-long loan deal. Reilly previously worked with the Par's manager Allan Johnston at the Doonhamers, where he helped the club to win the Scottish Second Division and also the 2013 Scottish Challenge Cup Final versus Partick Thistle in the 2012–13 season. Reilly's first appearance for the Pars was in a 3–0 victory at East End Park in the Scottish League Cup and his first goal arrived in a 2–1 defeat away to Hibernian at Easter Road. After the arrival of his former Queens strike-partner Nicky Clark from Bury at the end of August 2016, Reilly's remaining stints were restricted to second-half substitute appearances and Reilly ended that season with the club, having scored 2 goals in 28 appearances.
St Mirren
Reilly signed a one-year deal with Scottish Championship club St Mirren on 12 June 2017. Reilly scored 22 goals in 44 games for Saints, as he helped fire them to the Scottish Championship title. Reilly's contract with St Mirren was not renewed.
Bristol Rovers
In July 2018, Reilly departed the Buddies and signed for Bristol Rovers on a free transfer. On 22 September 2018, Reilly scored his first league goal for the Pirates in the 7th minute at home to Coventry City in a 3–1 win. In 2018/19 he featured in 35 competitive first team games of which he started 16 in the league and was brought on as substitute 14 times. He was substituted in 13 of those league games that he started. Similarly in cup games he started twice of which he was taken off once. He was also brought on as a substitute in 2 cup games. From the 35 games in which he played he scored 4 goals.
