At the age of sixteen - on the advice of his uncle and guardian, Charles Elstob, prebendary of Canterbury from 1685 to 1721 - he was sent to Catharine Hall, Cambridge, "in a station below his birth and fortune".
He was chaplain to Bishop Nicolson of Carlisle, who in February 1713 applied for Chief Justice Parker's influence for his appointment to the preachership at Lincoln's inn.
[4] Hickes wrote a preface to Elstob's Essay on the great Affinity and Mutual Agreement of the two professions of Divinity and Law, ... in vindication of the Clergy's concerning themselves in political matters.
Sir Andrew Fountaine acknowledges Elstob's help in giving descriptions of Anglo-Saxon coins for the tables published by him in Hickes's Thesaurus.
In 1709 he contributed a Latin version of the Anglo-Saxon homily on the nativity of St Gregory to the edition of the original prepared by his younger sister Elizabeth Elstob.
He also made proposals for what was to be his great work, a new edition of the Anglo-Saxon laws already published by William Lambarde (1568) and Abraham Wheelocke (1644), with many additions, comments, prefaces, and glossaries.
In Thomas Hearne's Collection of Curious Discourses by Eminent Antiquaries is a mock-heroic poem by Elstob upon the butler of University College.