He broke into the Celtic team in the late 1960s, as one of a generation of players who continued a highly successful era for the club.

Hay appeared in 27 international matches for Scotland, and was selected for their 1974 FIFA World Cup squad.

After playing for Scotland in the 1974 World Cup in West Germany, and following a dispute with Celtic, he was transferred to Chelsea for a club record £225,000.

Initially signed as a direct replacement for Alan Hudson in midfield, he adopted a more defensive role in the young Chelsea side that emerged following their relegation a year later.

Hay succeeded Billy McNeill as Celtic manager in 1983, winning the Scottish Cup in 1985 and the Premier Division in dramatic fashion in 1986.

Celtic won their final game 5–0 against St Mirren at Love Street but needed Hearts, who were league leaders and favourites to lift the trophy, to lose to Dundee at Dens Park.

In 1989, Hay ventured to Norway and led Lillestrom SK to the Norwegian Premier League championship.

Hay became chief scout at Celtic in 1994, and was responsible for identifying players such as Jorge Cadete, Paolo di Canio and Pierre van Hooijdonk who signed for the club.

Despite this success, the veteran boss was released at the end of the season to be replaced by Allan Preston, one of his first team coaches, by new chairman, Pearse Flynn of the Lionheart Consortium.