He was the son of a linen draper at Wakefield, Yorkshire. At the age of fourteen he entered University College, Oxford, and in 1693 he published notes on Plutarch's De audiendis poetis and Basil's Oratio ad juvenes. In 1694 he was elected fellow of Lincoln College, Oxford and in 1697 his edition of Lycophron appeared. It was followed by his Archaeologia graeca (2 vols. 8vo, 1697–1698), the popularity of which endured till the advent of Dr William Smith's dictionaries. A reprint of his Lycophron in 1702 was dedicated to Graevius, and the Antiquities was afterwards published in Latin in the Thesaurus of Gronovius.
In January 1737 Potter was unexpectedly appointed to succeed William Wake in the see of Canterbury. While in that seat, he continued to represent a High Church position, but he was also ineffective at restoring the Convocation. Alexander Pope attacked him in the 1743 version of his The Dunciad (book II, 323).
Potter died on 10 October 1747. His Theological Works, consisting of sermons, charges, divinity lectures and the Discourse on Church Government, were published in three volumes.