Esposito’s places of birth and death suggest a life in Italy, but contrary to that expectation he lived and worked in Dublin almost all his professional life, from 1882 to 1928. He had earlier been studying music at Naples and had moved to Paris five years before he came to Dublin. He was Professor of Composition at the Royal Irish Academy of Music, founded the chamber series at the Royal Dublin Society in 1886, founded and directed the Dublin Orchestral Society (1898-1914) and was active as pianist, concert promoter and adjudicator at musical competitions.
His music is rooted in the late-nineteenth-century romantic era, adding an unmistakable Irish overtone in many compositions using folk-song or dance material. Among his largest compositions are the opera The Tinker and the Fairy (1910), and Irish Symphony (1902) and the cantata Deirdre (1897). He also wrote for many chamber music instrumentations, piano music, songs and folk-song arrangements.