In 1963, during his first year at UCD, he was approached by the Rathmines and Rathgar Musical Society and played Jack Point in The Gaiety's production of The Yeomen of the Guard.
Glavin received his licentiate from the Royal Irish Academy of Music (RIAM) and joined the staff there in 1969.
His poetry appeared in numerous newspapers and journals and was first anthologised in Irish Poets 1924–74, edited by David Marcus.
Glavin's work of half a lifetime was the ambitious sequence of four-line poems, originally titled Living In Hiroshima.
When Anthony received his Arts Council bursary in 1990, his intention was to travel to Japan, to visit Hiroshima and Nagasaki and supplement his extensive research with actual experience.