Mulhare, as a young adult, began schooling at the National University of Ireland in medicine, but eventually decided upon a career in theatre.

[1] After acting in various Irish venues including the Gate Theatre in Dublin, he moved to London, where he worked with Orson Welles and John Gielgud.

In 1955 Mulhare starred as James Finnegan in the first feature film produced in Israel, Hill 24 Doesn't Answer.

He guest-starred in television programmes, including Daniel Boone and the Twelve O'Clock High episode "Siren Voices" as Luftwaffe Colonel Kurt Halland.

In 1969 Mulhare starred in Gidget Grows Up, an American made-for-television comedy film with Karen Valentine in the title role.

His final role was on Baywatch Nights alongside former Knight Rider co-star David Hasselhoff in December 1996.