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.