An open-side flanker, he played schools rugby for Blackrock College and then moved on to play senior rugby for UCD, before earning a call up to the Ireland team in 1970.
In 1971, he was a member of the British and Irish Lions squad that toured New Zealand, missing out on a start in the third Test due to illness.
Slattery toured with the Lions again in 1974, playing in all four Tests and captaining the side for two provincial matches.
He was captain of the most successful Irish touring side ever in 1979 which won 7 of the 8 matches in Australia, including the two Tests in Brisbane and Sydney.
In addition to the above honours, he was a member of the Irish Triple Crown-winning team in 1982.