Smith was admitted to St John's College, Cambridge on 12 June 1674 as a sizar, graduating B.A. 1677, and M.A. 1681. On leaving he was ordained deacon and priest of the Church of England by Archbishop Richard Sterne; in July 1682 he was admitted a minor canon of Durham Cathedral, was shortly afterwards collated to the curacy of Croxdale, and on 1 July 1684 to that of Witton Gilbert. From 1686 to 1689 he acted as chaplain to Lord Lansdown, the English ambassador at Madrid. In 1694 he was appointed domestic chaplain to Nathaniel Crew, who in the following year collated him to the rectory and hospital of Gateshead, and on 25 September 1695 to the seventh prebendal stall in Durham Cathedral.
