Slattery plays club rugby for Blackrock College and University College Dublin before embarking on an international career that takes in 61 caps for Ireland, 18 as captain, and four for the British and Irish Lions. He makes his international debut in a draw against South Africa at Lansdowne Road in 1970.
In 1971, Slattery first tours with the British and Irish Lions squad that toured New Zealand, missing out on a start in the third Test due to illness. With the back-row berths claimed by John Taylor, Peter Dixon and Mervyn Davies and still being a newcomer at international level he has to wait until 1974 for his shot at a Lions Test jersey. In the meantime, he plays for the Barbarian F.C. in the famous 1973 game against the All Blacks in Cardiff.
Slattery tours with the Lions again in 1974, playing in all four Tests and captaining the side for two provincial matches. In South Africa he is an invaluable member of the touring party that comes to be known as “the invincibles.” He starts all four Tests as the Lions win the series 3-0 and skippers the side twice during midweek tour matches.
For Ireland, Slattery captains their hugely successful touring side in Australia in 1979 when they win seven of the eight matches including the two Tests in Brisbane and Sydney. In 1982 he starts all four games of Ireland’s Triple Crown season, being denied the Grand Slam by France in the final game of the Five Nations Championship.
Slattery is inducted into the International Rugby Hall of Fame in 2007.