Born Robert Dundas, he was the eldest son of Philip Dundas (c1763–1807, the fourth son of Robert Dundas of Arniston, the younger), and Margaret daughter of Sir John Wedderburn, 6th Baronet (1729–1803) (and sister of Sir David Wedderburn, 7th Baronet (1775–1858)).
He served as Chancellor of the Duchy of Lancaster under the Earl of Derby between March and December 1852. Nisbet-Hamilton was returned to Parliament for Ipswich in 1827, a seat he held until 1831 and again briefly in 1835. He also represented Edinburgh between 1831 and 1832 and North Lincolnshire between 1837 and 1857.
When the Conservatives came to power under the Earl of Derby in 1852, Nisbet-Hamilton was appointed Chancellor of the Duchy of Lancaster and sworn of the Privy Council.
He remained as Chancellor of the Duchy of Lancaster until the government fell in December 1852. In 1833 he was elected a Fellow of the Royal Society.
Nisbet-Hamilton married Lady Mary, daughter of General Thomas Bruce, 7th Earl of Elgin and Mary, daughter and heiress of William Hamilton Nisbet, in 1828. They had one daughter.
Lady Mary died in December 1883.
Nisbet-Hamilton survived her by four years and died in June 1887.
Royal Society; 8th United Kingdom Parliament. 9th United Kingdom Parliament. 10th United Kingdom Parliament.
11th United Kingdom Parliament.
13th United Kingdom Parliament. 14th United Kingdom Parliament.
15th United Kingdom Parliament. 16th United Kingdom Parliament.
