However, he signed for Town's rivals Norwich City and made his league debut for them on 25 August 1984 in a 3–3 draw against Liverpool. His first goal for Norwich came on 10 November 1984 in a 3–0 win against Luton Town. Gordon made 27 appearances during that 1984–85 season. He found first-team opportunities limited during the following 1985–86 season but did score the goal that secured the Division 2 championship for Norwich in a 1–1 draw against Stoke City on 19 April 1986. 1986–87 was Gordon's breakthrough season. He established himself as a first-team regular and played 41 league games as a vital part of the team that recorded what was then their best ever league finish of fifth position – though he was denied the chance to play in the UEFA Cup due to the ban on English clubs in European competitions arising from the Heysel disaster of 1985. Gordon was capped by England under 21s towards the end of the campaign, but hampered his chances of future selection when he and his Norwich City teammate Robert Rosario broke curfew while away with the under 21s and went to a nightclub. Gordon was later capped twice for the England B team, but never played for his country at senior level. In December 1988, Gordon achieved "a unique place in Norwich City history – a record nobody can ever take away. He was the first player to score in a live televised Football League match involving the Canaries", a 2–1 win over West Ham. The 1988–89 season ended with Gordon being voted Norwich City player of the year as the team finished fourth in the league and reached the semi-finals of the FA Cup, though again he and his colleagues were deprived of UEFA Cup action as the ban on English clubs in European competitions was still in force. In total, Gordon played 261 games for Norwich between his 1984 debut and his final appearance on 2 November 1991. After the match against Nottingham Forest on 2 November 1991, he signed for Scottish club Rangers for a fee of £1,200,000.
He joined West Ham United for £750,000 on 8 July 1993, but his career at Upton Park was disrupted by injuries. He did, however, score West Ham's first ever goal in the Premier League, in a 1–1 draw against Coventry City, on 21 August 1993 at Highfield Road, his only West Ham goal. In just over three years he made only 11 appearance in all competitions for West Ham and had a six-game loan period, in 1996, at Millwall before leaving to join Bournemouth in August 1996 on a free transfer. In 1996, Gordon expressed a desire to return to Norwich City, but his injuries got the better of him and he retired as a professional player in February 1997.
After football
Coaching
After retiring Gordon set up an academy in the Great Yarmouth and Lowestoft area. He was appointed manager of Great Yarmouth Town in May 1997, before becoming Director of Football at Gorleston in November 1998. He made a brief playing comeback, before being appointed manager in 1999. In 2000, he left Gorleston and set up an Ipswich Town academy in Lowestoft. He later started an independent football school, before returning to Great Yarmouth Town as Director of Football in October 2007. In 2013, he was appointed Director of Football at IFA Sport in the United Arab Emirates.
Family
In 2007, Gordon mentioned in a newspaper interview that his young son Remy is training with Norwich and on 29 July 2009 it was confirmed that Remy Gordon signed a scholarship with Norwich City Football Club, following in his father's footsteps.
Business
In 2008, Gordon was reported to be running his own "Legends" lounge bar in Yarmouth and his own soccer academy.
