Rea turned professional in 1984, recording his first victory over Jack Fitzmaurice in the Grand Prix. He reached the last 32 of this tournament, losing 1–5 to David Taylor. A run to the last 48 at the United Kingdom Championship followed this, but Joe Johnson eliminated Rea 9–6 at this stage.
Several quiet years ensued, but the 1988/1989 season provided an upturn in form for Rea.
A run to the last 32 at the International Open - where he lost 4–5 to Taylor - was followed by the only professional title of his career - the 1989 Scottish Professional Championship. He defeated Murdo MacLeod 9–7 in the final.
This performance appeared to spur Rea on, and in the 1989 World Championship, he defeated Dennis Hughes 10–3, Pat Houlihan 10–5 and Ray Edmonds 10–7 to reach the last 48. Requiring one more victory to make his debut at the Crucible Theatre, Rea was drawn against Steve James but, despite recovering from 2–9 to trail only 7–9, he lost the match 7–10.
By 1990, Rea himself was in decline, his last performance of note being a run to the last 32 at the 1992 United Kingdom Championship, where he beat David Rippon, Brian Cassidy, Les Dodd and Tony Jones before losing 9–3 to Jason Ferguson.
In 2012 and 2015, he entered the World Seniors Championship, losing to Bill Oliver in the former and Mark Davis in the latter. Rea owns the Lucky Break snooker club in Clydebank, through which he has sponsored local football teams. Guests at Rea"s club have included John Higgins and Stephen Maguire.