He graduated Bachelor of Arts on 30 April 1610 and Master of Arts He was magister puerorum in 1620, and senior bursar in 1622. Graduated Bachelor of Divinity and received a preacher"s license on 9 March 1621, and proceeded Doctor of Divinity on 17 February 1627.
He matriculated at Queen"s on 11 July 1606, aged 15, having entered the college in the previous Easter term. He was elected taberdar (pauper puer) on 29 October 1609. on 8 July 1613, became chaplain on 5 July 1613, and fellow on 22 March 1614-1615. On his uncle"s resignation of the headship of Queen"s (17 June 1626), he was elected Provost.
He now attached himself to Laud, and was made chaplain in ordinary to Charles I. In the first year of his provostship, with the assistance of Sir Thomas Coventry, Viscount Doncaster, and Sir George Goring, vice-chamberlain to Queen Henrietta Maria, he obtained the advowson of three rectories and three vicarages in Hampshire for the college.
He himself received the rectory of Strathfieldsaye in 1627, and after the death of William Cox in 1632 was made precentor of Chichester. He received the rectory of Bletchington, Oxfordshire, in 1631.
During Laud"s chancellorship of the university, Potter was a frequent correspondent. He was a disciplinarian in his college, and instituted expositions of the creed on Sundays in chapel and English sermons on Thursdays.
In 1631, on the death of John Rawlinson, principal of Saint Edmund Hall, he successfully asserted the rights of his college against the claim of the chancellor to nominate a principal, and Laud admitted and confirmed the right.
He had now attracted notice as a prominent Arminian, and was attacked in a violent sermon written under the influence probably of John Prideaux. Potter took much the same line as Laud had taken in his reply to John Fisher. A second edition (London, 1634) was revised by Laud, whose suggested alterations later formed one of the charges brought against him at his trial.
He became pro-vice-chancellor on 13 July 1639, and was appointed vice-chancellor on 28 July 1640.
lieutenant was to him that Laud"s letter of resignation of his office was addressed. He had been promoted, by Laud"s influence, as Dean of Worcester in 1636, and he received the rectory of Great Haseley, Oxfordshire, 1642.
On the outbreak of the First English Civil War he contributed £400 to the king in July 1642, in addition to £800 given by the college. He left Oxford, but returned before Christmas 1642.
He preached at the Treaty of Uxbridge.
In January 1646 the king nominated him to the deanery of Durham, but he died, before his installation, on 3 March. Potter married Elizabeth, daughter of Doctor Charles Sonnibanke, canon of Windsor, by whom he had a son Charles Potter (1634–1663), courtier, born in the college in 1634. Charles became a Roman Catholic, and at the Restoration was made an usher to Queen Henrietta Maria.
In May 1662 he was repaid £2,000 which his father had lent to Charles I. Elizabeth afterwards married Gerard Langbaine, the next Provost of Queen"son
On 4 December 1640 he found it necessary, with the other university officials, to issue a notice denying that they knew or suspected "any member of the university to be a papist, or popishly inclined".