Born in Dundonald, McClure studied at Campbell College, then at Queen's University, Belfast. He first graduated in medicine, then in pathology, bacteriology and biochemistry. In 1932, he became a Fellow of the Royal College of Surgeons of Edinburgh, and in 1944, a Fellow of the Royal College of Obstetricians and Gynaecologists. In 1937, he began lecturing at Queen's.
At the Northern Ireland general election, 1962, McClure was elected for the Ulster Unionist Party in the Queen's University seat. He held his seat at the 1965 general election, but it was abolished from the 1969 election. He was instead elected to the Senate of Northern Ireland, and served until it was prorogued in 1972.
- "Obituary: H. I. McClure", British Medical Journal, vol. 284, 20 March 1982
- Biographies of Members of the Northern Ireland House of Commons