Herron joined Celtic as a youth player aged 8. Whilst a member of the club’s development squad, Herron, aged 18, made his first team debut for Celtic on 22 December 2012, coming on as an 83rd-minute substitute in a Scottish Premier League match against Ross County, replacing Georgios Samaras in a 4–0 win. Herron did not feature in a competitive first team game again until over a year later when he made his first starting appearance, in a league match away against Motherwell on 19 April 2014.
On 23 January 2015, Herron signed for Scottish Championship club Cowdenbeath on loan until the end of the 2014–15 season. He made 5 appearances for the Miners, picking up three yellow cards.
Upon his return to Celtic, he was released from his contract.