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.&lt;ref name="2013/14"&gt;&lt;/ref&gt; His debut at the main stage of a ranking event came at the Indian Open by seeing off Kurt Maflin 4–2. In New Delhi he lost 4–2 to Mark Davis. 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. He finished his first season on tour ranked world number 112.