Articled to Sir Charles Lanyon, Drew joined the office of William G. Murray and moved to Dublin. He became one of the most distinguished architects of the 19th century in Ireland, as well as being president of the RIAI and held the Chair of Architecture at the new National University of Ireland. Amongst his most important buildings are the Ulster Bank branch of Dame Street, Dublin (the interior of which has been destroyed); the Trinity College Graduate’s Building, Rathmines Town Hall, and St Anne’s Cathedral in Belfast.
He was inaugural President of the Royal Society of Ulster Architects, serving from 1901-1903. In addition, he was President of the RIAI, the RSAI and the RHA and held the chair in architecture at the National University of Ireland.
He married Adelaide Anne, sister of William G. Murray, in 1871. In his latter years Drew suffered from gout. He was affected by it in 1909, but returned to work by the beginning of 1910. In February 1910 he underwent an operation for appendicitis which left him in a critical condition, and he died on 13 March.