His family moved to London, where Elmore studied at the Royal Academy of Arts. His early works were in the troubadour style of Richard Parkes Bonington, but he soon graduated to religious work, notably The Martyrdom of Thomas à Becket, commissioned by Daniel OConnell for Westland Row Church in Dublin. Between 1840 and 1844 Elmore travelled across Europe, visiting Munich, Venice, Bologna, and Florence.
Elmore seems to have been associated with The Clique, a group of young artists who saw themselves as followers of Hogarth and David Wilkie. According to his friend William Powell Frith he was member of the group, but since it was most active while he was in continental Europe, his involvement was probably short-lived.