He became known by the courtesy title Lord Kennedy when his father succeeded to the earldom of Cassilis in 1792.

In 1820, King George IV made Archibald a knight of the Order of the Thistle.

He and 13 others established the Ayr Gold Cup held annually with only Scottish-trained horses that raced over a two-mile (3.2-kilometre) run.

They had six children:[4][5] Lord Ailsa died in 1846 and was succeeded by his grandson Archibald Kennedy.

[5] Lord Ailsa bought a house near Twickenham in London that had previously belonged to the playwright Richard Brinsley Sheridan.