Born in Belfast, Hamilton began his career at Distillery, before moving on to Linfield. He was named Ulster Footballer of the Year and Northern Ireland Football Writers' Association Player of the Year for the 1970/71 season, also finishing as Irish League top goalscorer. In 1971, he signed for Ipswich Town, where he spent five years and made over 150 appearances for the club. In 1976, he signed for Everton, before moving onto short spells at Millwall and Swindon Town.
In the FA Cup semi-final of 1977, full-time was looming in the clash between Everton and local rivals Liverpool at Maine Road, with the score at 2–2, when Hamilton put the ball into the back of the net. However, infamously, his goal which should have stood was disallowed by referee Clive Thomas and the match went to a replay, which Everton lost 3–0. This echoed an incident in the 1975 FA Cup semi-final replay, when Thomas had similarly disallowed a potentially match winning goal by Hamilton.
Everton supporters felt legitimately aggrieved to have victory snatched away
The FA Cup was shown on BBC and ITV in 1977 and the first game of the semi-final which was drawn 2–2 is also memorable for the fact that in a highlights programme the referee was asked to explain the disallowed 'goal' but he failed to explain and all he would say was.....There was an offence
Hamilton's time at Everton will always be remembered for that controversial disallowed goal in the FA Cup semi-final, however, when Hamilton signed for Everton the manager was another Northern Irishman Billy Bingham but when Bingham lost his job as manager Hamilton's first team opportunities became more and more limited
Scores and results list Northern Ireland's goal tally first.
Hamilton became player/manager of Tranmere Rovers in 1980. The club remained in the Fourth Division throughout this period, with three top half finishes during his five-year period in charge, culminating in a finish of 6th in 1984–85.
He was appointed manager of Wigan Athletic in 1985. The 1985–86 season saw Wigan emerge as contenders for promotion to the Second Division, a feat which looked likely for virtually the entire campaign. However, when Wigan had completed their fixtures Derby County had three games in hand, two of which would be won to pip the Latics by a single point. His achievements with Wigan did not go unnoticed, and he would move to Leicester City soon afterwards. However, he was unable to keep Leicester in the First Division and soon left the club, and returned to Wigan as manager from 1989–1993.
Hamilton was appointed manager of Northern Ireland in 1994, succeeding Billy Bingham. In the Euro 96 qualifiers, Northern Ireland were in contention for qualification and were only narrowly pipped to second place by the Republic of Ireland. The 1998 World Cup qualifiers provided a far worse return despite a promising early draw with Germany – who would later beat Northern Ireland for the first time in two decades – and Hamilton left the job at the end of the qualifiers.
In April 2000 he was appointed manager of Norwich City, but resigned on 4 December. He returned to Ipswich as coach in 2001, but left the club in 2002. In November 2006, he was appointed Technical Director of the Antigua and Barbuda Football Association.
Hamilton is now a media pundit working mainly with Eurosport, BBC Radio 5 Live, Setanta Sports, Today FM, Sky Sports and Anglia Television.