Henry was born in February 1692,[2] the third and youngest son of Gustavus Hamilton and his wife Elizabeth Brooke.
[7] He held that seat during the entire duration of the parliament from 12 November 1715 to 11 June 1727 when it was dissolved by the king's death.
[12] Hamilton did not contest the Irish election of 1727, which was held for the only Parliament of King George II, which lasted from 14 November 1727 to 25 October 1760.
However, in 1730 he contested and won the by-election for one of the two seats for County Donegal that resulted from the death of Alexander Montgomery on 19 December 1729.
[14] His father and his two older brothers Frederick and Gustavus had also represented County Donegal in the House of Commons.