Muir turned professional in 2013 after graduating from event two of the Q School, defeating David Morris 4–0 in the final round. Junior career
His first wins came in qualifying for the next event, the Australian Goldfields Open, by defeating James Cahill and Rod Lawler both 5–1, before losing 5–2 to Liam Highfield. At the Asian Tour event, the Zhangjiagang Open, he defeated world number seven Ding Junhui 4–3 in the last 32 by compiling a break of 80 in the final frame, before being whitewashed 4–0 by Da Hailin in the next round.
Muir finished his debut season on the main tour at world number 113.
Muir failed to qualify for a ranking event during the 2014/2015 season. All 128 players on the tour automatically play at the venue stage of the United Kingdom Championship and Welsh Open, with Muir being knocked out in the first round 6–5 by Peter Ebdon and 4–1 by Michael White respectively.
Muir would be relegated from the snooker tour as he is finished the season as the world number 99. As the snooker tour regularly visits China, Muir takes lessons in Mandarin so he is able to conduct interviews in the local language.
He was a goalkeeper in his childhood and was scouted by Celtic, but a recurring wrist injury forced him to give it up.
Muir is also a keen tennis player. Amateur finals:: 2 (1 titles).