Since retiring as a player, Murphy has remained involved in rugby union, both as a coach and administrator.
Both his father, Noel Sr, and his son Kenny Murphy have also represented Ireland at rugby.
[3][4] His Ireland career ended in controversial circumstances when he was involved in a punch up with Welsh lock Brian Price[5][6] Murphy also toured twice with the British and Irish Lions and was a member of their squad for both the 1959 and 1966 tours of Australia and New Zealand.
He played in 18 games during the 1959 tour and a scored further four tries, one each against Canterbury and Bay of Plenty/Thames Valley and two against North Auckland.
He is currently one of Ireland's representatives on the International Rugby Board and is on the organising committee of the Heineken Cup.