He joined the main snooker tour in May 2013 after he won through the 2013 Q School courtesy of a 4–0 victory over Chris Wakelin.

[2] Slessor's first wins as a professional were at the qualifying rounds of the 2013 Australian Goldfields Open 5–4 against Jamie Clarke and 5–2 against Cao Yupeng, before losing 5–2 to Simon Bedford.

Slessor also suffered first round exits at the UK Championship and Welsh Open 6–2 to Liang Wenbo and 4–1 to Stephen Maguire respectively.

[6] He then raced into a 3–0 lead over Matthew Selt and held on to beat him 5–3 and play in the last 32 of a ranking event for the first time in his career.

[13] In Indian Open, Slessor got to the quarter-final, by beating Alan McManus 4–3, Joe Perry 4–3, by leading 3–0, Shaun Murphy 4–1, before losing Mark King 2–4.