[6] Muir won a place on the main snooker tour for the 2013–14 season after coming through the second event of the 2013 Q School, defeating David Morris 4–0 in the final round.

[7] 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.

[7] 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.

All 128 players on the tour automatically play at the venue stage of the UK Championship and Welsh Open, with Muir being knocked out in the first round 6–5 by Peter Ebdon[10] and 4–1 by Michael White[11] respectively.

Muir threatened a comeback in the opening round of the World Championship qualifiers when he rallied from 9–4 down against Cao Yupeng to win four successive frames, but lost the next to be beaten 10–8.

[23] In the 2018 European Masters, Muir reached the last 16 defeating Martin Gould 4–2, Lee Walker 4–2, Gary Wilson 4-2 before losing to Mark Allen 4–3.

After defeating defending champion Neil Robertson 4–2 in the second round of the 2018 Scottish Open, Muir revealed he is prone to Retinal migraine issues.