[2] He made his first-team debut in March 1975, at home to Stoke City, and would go on to form a potent striking partnership with Malcolm Macdonald; the two scored 46 goals between them in 1976–77.

Stapleton went on to move to Manchester United in the summer of 1981 for £900,000 (a fee set by tribunal after the two clubs could not agree) as new manager Ron Atkinson began building a team capable of challenging for silverware after a disappointing 1980–81 season under Dave Sexton.

Stapleton then played on loan for three months with Derby County before heading to the European Championships in 1988 as the captain of the Republic of Ireland side, which beat England, drew 1–1 with the Soviet Union, eventual runners-up, and lost by a single late goal to tournament winners, the Netherlands.

He then played for French club Le Havre for a season, before returning to England again with Blackburn Rovers in 1989, followed by moves to Aldershot, Huddersfield Town (as player-coach) and Bradford City.

Stapleton captained the Irish team to the 1988 Euro finals and played in all of their matches during the competition including Ireland's famous victory against England.

After the 1988, European Championships Stapleton remained on the fringe of the national team during qualification for World Cup Italia 1990 making just two appearances late in the campaign.

The Bolton manager Sam Allardyce wanted Stapleton to enhance the skills of the strikers at the club and saw the Irishman as an ideal candidate, given his successful playing career.

His sister Helena played for the Republic of Ireland women's national football team in the 1980s [9] He is second cousin of Irish actor Barry Keoghan.