Born in England, he played for the Republic of Ireland, winning 29 caps including 3 in Euro 88.
On 3 February 1979, he made his debut in the 3–0 home defeat to Manchester City highlights of which was shown on The Big Match.
Around 1981 he became a regular with his strength in wing play being that he was difficult to knock off the ball and was able to put in accurate crosses.
Galvin tried to make a fresh start at Swindon Town, where he was signed by former Spurs teammate Ossie Ardiles in 1989.
He was named by Jack Charlton in Ireland's first ever finals squad at Euro 88, and started all 3 games against England, USSR and the Netherlands.