In 1768, Hamilton became member of parliament for Lancashire and held the seat until 1772 when he was appointed a Steward of the Chiltern Hundreds.

In 1799, he inherited his half-nephew's titles and was appointed his successor as Lord Lieutenant of Lanarkshire.

Hamilton was a prominent figure in the world of Thoroughbred horse racing.

[1] On 25 May 1765, he married Lady Harriet Stewart (a daughter of the 6th Earl of Galloway) and they had five children: The duke died in 1819 and was succeeded by his eldest son.

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