He was educated at Eton and Oriel College, Oxford and graduated B.A. on 12 October 1704, being elected a Fellow of All Souls' in the same year, and created D.C.L. on 29 August 1735. He received the Lambeth degree of LL.B on 26 April 1714, and at about the same time was nominated by his father to the chancellorship of the diocese of Oxford, which he retained until his elevation to the woolsack. Talbot was at first destined for the Church, but, by the advice of Lord Cowper, exchanged divinity for law, and was admitted on 28 June 1707 as a student at the Inner Temple, where by special grace, before he had completed the full number of terms then required, he was called to the Bar on 11 February 1710-11. On 31 January 1718-19 he was admitted a member of Lincoln's Inn, of which society he was elected in 1726 as bencher, treasurer, and master of the library. On 31 May 1717 he was appointed solicitor-general to the Prince of Wales. In 1719-1720 he represented Tregony, Cornwall in parliament and in the parliaments of 1722-7 and 1727-32 he represented Durham. In the meeting of Parliament, 9 October 1722, he supported the nomination of the Prince's favourite, Sir Spencer Compton (afterwards Earl of Wilmington), for the speakership of the House of Commons. In 1726 Talbot was appointed solicitor-general to King George I and continued in the office on the accession of George II the following year.

On 29 November 1733, with a great reputation for legal learning and accomplishment, he succeeded Lord King as Lord Chancellor, and was sworn of the Privy Council. Raised to the peerage as Baron Talbot of Hensol, Glamorganshire, 5 December 1733, he took his seat in the House of Lords on 17 January 1733-4, and, after giving proof of high judicial capacity, died of heart disease at his house in Lincoln's Inn Fields on 14 February 1736-7.