Gillespie made his debut for Manchester United in the 1992-93 season, and scored his first goal for the club against Bury in a 2-0 FA Cup third round triumph on 5 January 1993.
Occasional appearances for United followed over the next two years, but he was never able to displace Andrei Kanchelskis as United's first-choice right winger.
After a loan spell at Wigan Athletic in 1993-94, he moved to Newcastle United on 10 January 1995, as a £1million component in the 7 million deal (£6million cash) which took Andrew Cole to Old Trafford. Ironically, Gillespie had scored one of United's goals against Newcastle in the 2-0 victory at Old Trafford which had knocked Kevin Keegan's side off the top of the Premier League table less than three months earlier.
Meanwhile, Gillespie stayed at Newcastle for three-and-a-half years and during this time he played 143 games, including 15 European ties (in both the Champions League and UEFA Cup) and scored 13 goals. In both the 1995-96 and 1996-97 seasons he helped Newcastle to finish second in the Premier League (runners up to Gillespie's former club, Manchester United, on both occasions), being a key member of "The Entertainers".
In his final full season at Newcastle, the 1997-98 season, Gillespie helped Newcastle to reach the FA Cup final. However, he was not in the squad for the final and Newcastle lost to Arsenal The following season saw Gillespie depart Tyneside in a £2.3million move to Blackburn Rovers.
On 20 January 2007, during a Premiership match against Reading at the Madejski Stadium, Gillespie was sent off for violent conduct (elbowing Reading's Stephen Hunt) twelve seconds after coming on as a substitute. As he made his way off the pitch, Gillespie pushed Hunt in the face. He thereby achieved the dubious honour of becoming the fastest sending-off of a substitute in English football. He was sent off before the ball had come back into play, and so technically sent off being on the pitch for zero seconds of play.
The day after this incident, he stunned Sheffield United when he handed in a transfer request to the chief executive Terry Robinson.
In the summer of 2007 he was linked with a move back to the Premiership with Bolton Wanderers but, in July, Gillespie signed a new two-year contract.
In July 2008 he limped out of a pre-season friendly at Bury and is likely to miss the start of the 2008-2009 season Recently been linked to an Australian team Central Coast Mariners. Gillespie has since been told he is free to leave the club after a fall out with Kevin Blackwell