He matriculated at St Mary Hall, Oxford on 23 February 1741, knighted into the Order of the Thistle in or around 1742, and created a DCL on 14 April 1743.

[1] On 14 February (St. Valentine's Day) 1752, Hamilton met the society beauty Elizabeth Gunning at Bedford House in London.

According to Horace Walpole, the duke wished to marry her that night and he called for a local parson to perform the ceremony.

He died on 17 January 1758, aged 33, at Great Tew, Oxfordshire from a cold caught whilst out hunting.

The Duke was hereditary keeper of the Palace of Holyroodhouse in Edinburgh, but all but his apartments in the building had been reduced to a state of dereliction by the time of his death.