MRCS Eng LRCP Lond 1941; DA Eng 1947.
Conroy studied at Manchester and was house physician at Withington Hospital Manchester. After serving in the RAMC, Conroy was visiting anaesthetist at a number of hospitals in Manchester and Lancashire, before being appointed anaesthetic registrar at Ancoats Hospital Manchester. Conroy was a member of Association of Anaesthetists of Great Britain.