As a military officer, he served in both the British and French armies, as well as taking part in Jacobite rebellions in 1715 and 1745, and spent nearly 20 years in exile on the Continent.

Arthur had three half-brothers from his father's first marriage; Hugh, Master of Balmerino, who died in 1708 at the Siege of Lille, James (1675–1746), a lawyer and judge, and Alexander (d.

[2][3][b] He was not initially expected to inherit the family estate and embarked on a military career, being commissioned a captain in Lord Shannon's regiment in March 1714.

Alongside David Wemyss, Lord Elcho, he was given command of a troop of Charles' "Life Guard"; unlike nearly all other senior Jacobites, he escaped any criticism in the post-rising memoirs by various participants.

[7] John Daniel, a colleague in 1745, recorded that Elphinstone's "sole and predominant passion" was "hard drinking", but paid tribute to his loyalty, courage, and gift for languages, noting that "his memory for his years was wonderful".

[9] Horace Walpole, in a letter, described him as "the most natural brave old fellow I ever saw [...] at the bar he behaved like a soldier and a man: in the intervals of form, with carelessness and humour".

[10][8] Like Kilmarnock, he was buried in the Church of St Peter ad Vincula in the Tower of London: reportedly, at his request, alongside William Murray, Marquess of Tullibardine.