He spent the rest of the 1977/78 season in the City reserves but was given his chance at the beginning of the following season making his debut on the 19 August '78 in a 2-1 win over Middlesbrough at Ayresome Park, he went on to make a further 14 league appearances before the end of the season.
A lot of admirers courted Gillespie's skills and attributes as a player, especially as he was a player who was involved in numerous, successful, relegation battles with Coventry for six seasons, he ultimately got his big move and it was Liverpool that got his signature on 8 July 1983 for £325,000. He was the first signing to be made by new manager Joe Fagan.
Gillespie firmly established himself in the first team the following year, when he missed just three league games all season. By 1988, when he partnered Hansen in all bar five of Liverpool's games in the league, the Anfield club were a cut above every other side, losing just twice and coasting to the title. Gillespie weighed in with his share of goals too, including one in the famous 5-0 hammering of Nottingham Forest, which critics, including the great Tom Finney, describe to this day as the finest domestic performance by any English club.
A week before Liverpool were scheduled to face Wimbledon in the FA Cup final to try to secure their second "double", Gillespie and teammate Nigel Spackman clashed heads when leaping for the same ball in a league game against Derby County. Both suffered deep cuts, but were deemed fit for the game at Wembley and were each given customised protective bandages with red and white stripes to wear during the game. Gillespie was regarded as one of Liverpool's better players on the day. BBC summariser Jimmy Hill said: "Gillespie's been brilliant, headband or not," but Liverpool surprisingly lost 1-0.
In 1989, Gillespie joined his teammates in mourning the passing of 96 Liverpool fans at the Hillsborough disaster, during a year in which he again was a regular feature in the team. This time fortunes were reversed - Liverpool won the FA Cup with an emotional victory over fierce Merseyside rivals Everton, but lost the League title to Arsenal with pretty much the last kick of the season. Gillespie missed that game, however.
Gillespie won another league title with Liverpool in 1990, though his appearances record was diminishing, owing to the arrival of Swedish defender Glenn Hysen at Anfield. The following year, with Kenny Dalglish replaced as manager by Graeme Souness, after 214 appearances and 16 goals Gillespie was sold to Celtic F.C. for £925,000. His debut for the Glasgow club came on 17 August 1991, in a 4-1 league win over his former side Falkirk at Parkhead. Gillespie also managed to find the back of the net. He made 67 appearances for the Parkhead club over three years, before winding down his career back at Coventry, making three Premiership appearances during the 1994/95 season.
Gillespie won 13 caps for Scotland, Andy Roxburgh gave him his debut on 14 October 1987 in the 2-0 UEFA European Championship qualifier victory over Belgium at Hampden Park. He was selected for the squad that went to the 1990 FIFA World Cup in Italy, but his only appearance came on 20 June against Brazil at the Stadio delle Alpi Turin, a game the Scots lost 1-0. They failed to progress past the group stages.
Since retirement, Gillespie serves regularly as an expert summariser for Liverpool matches on BBC Radio Merseyside and is a regular member of the commentary team for Liverpool games on the official Liverpool FC TV channel LFC TV. He also continues to represent Liverpool in their veterans' side.
Gary is still held in high regard among the Anfield faithful, who voted him No.68 in the 2006 poll 100 Players Who Shook The Kop compiled by the official Liverpool Football Club website.