Aged 16, he reached the quarter finals of the U21 World Snooker Championships. He has been Irish champion at every level, winning the overall National championship every year from 2004 to 2006 (becoming the youngest ever winner in 2004). For 2006–07 he made his debut on the main tour, reaching the last 64 in two tournaments.
His best run in the 2007–2008 season was to the last 48 of the UK Championships, where he lost to Dave Harold (who also defeated him in qualifying for the previous year’s Welsh Open). His only opening-round defeat that year was to Supoj Saenla in the World Championship, but despite this setback in the highest ranking-point event of the season he did enough to reach the top 64 of the rankings. He also won the Lucan Racing Irish Classic, an event staged by Fergal O’Brien featuring 8 (mostly Irish) professionals – Morris beat O’Brien 5–3 in the final.
In qualifying for the 2008/2009 Bahrain Championship Morris defeated countryman Rodney Goggins and Adrian Gunnell to reach the final qualifying round, where he lost 0–5 to Michael Holt, scoring just 10 points in the process (the lowest in a match of five or more frames since 1992)
He made an important breakthrough at the World Open by beating Robert Milkins 3–1 and Ben Woollaston 3–0 to qualify for the televised stages of an event for the first time. However, he was drawn against the current world champion Neil Robertson losing 3–1.
Morris left his best run of results in the ranking events until the last tournament of the season, the World Championship. He beat Kacper Filipiak, Mark Joyce and Alan McManus before losing to Barry Hawkins 4–10 in the final qualifying round. He played in 11 of the 12 PTC events throughout the season, with his best finish coming in Event 9 where he reached the last 16. He was placed 66 on the PTC Order of Merit and finished the season ranked world number 71, outside of the top 64 who automatically retain their places on the tour for the 2012–13 season.