In 1660, Murray became a privy councillor, obtained a charter of the hereditary office of sheriff of Fife and in 1663 was appointed Lord President of the Court of Session.
In 1670 he succeeded to the earldom of Tullibardine on the death of his cousin, the 4th Earl and was created Marquess of Atholl and Viscount Glenalmond on 7 February 1676.