He was the second son of Thomas Thynne, 2nd Viscount Weymouth (1710–1751) by his second wife Louisa Carteret, daughter of John Carteret, 2nd Baron Carteret, 2nd Earl Granville (1690–1763). He was thus the younger brother of Thomas Thynne, 3rd Viscount Weymouth, later created Marquess of Bath.
He was educated at, Cambridge, graduating Bachelor, and in 1753 proceeded Master of Arts. In 1769 he was awarded the degree of Doctor of Civil Laws.
He was hereditary Bailiff of Jersey 1776–1826. William Leveson-Gower (died 1756). In 1761 he was elected for the Herefordshire borough of Weobley, which he represented until 1770.
He lost this office when the Grenville government fell in 1765, and entered into opposition.
This was worth £3000 per year, and he thereupon retired from the House of Commons. He also succeeded him as Bailiff of Jersey, a post (for life) long held by heads of the Carteret family.
In 1784 he was created Baron Carteret, of Hawnes, thus reviving his uncle"s second title. Hawnes Park was modernised and partly rebuilt by Henry Carteret, 1st Baron Carteret, and in 1813 consisted of two quadrangles.
He rebuilt the south front in about 1785-1790, probably to the designs of James Lewis.
In 1813 Lysons reported that it contained portraits of Margaret, Countess of Lennox. The mother of Rembrandt. Sir George and Lady Carteret.
John, Earl Granville, and at the foot of the staircase "an ancient view" of Longleat, seat of the Thynne family.
His simple white marble mural monument with bust survives in Kilkhampton Church, Cornwall, inscribed: "Henry Frederick Thynne. Born November 1735. Privy Counsellor, Bailiff of Jersey, Baron Carteret of Hawnes.
Died June 1826".
11th Parliament of Great Britain. 12th Parliament of Great Britain. 13th Parliament of Great Britain]
He was made a member of the Privy Council in 1770.
