He was the eldest son of John Hunter, Laird of Knapp and his spouse, Euphemia Jack of Longforgan, Perthshire, Scotland.
In 1789, Hunter, after leave in England, was appointed acting Superintendent of British Honduras in 1790, following the suspension of incumbent Edward Despard.
He returned to England in 1793 and was given the rank of colonel serving in Europe and then the Caribbean before becoming a military governor in County Wexford, Ireland following the Irish Rebellion of 1798.
On 10 April 1799, Hunter was appointed Lieutenant Governor of Upper Canada, succeeding John Graves Simcoe.
Alexander Grant became administrator of Upper Canada and continued Hunter's policies until a new lieutenant governor, Francis Gore, arrived from Britain in August 1806.