He became a Baron of the Scots Exchequer and was a friend of Prime Minister Lord Bute and David Hume.

[1][2] Mure was born late in 1718, the eldest son and successor to William Mure of Caldwell in Ayr and Renfrewshire, by his wife Anne Stewart, daughter of Sir James Stewart (1635–1713),[3] Lord Advocate, and widow of James Maxwell of Blawarthill.

[2] Mure graduated from Glasgow University in 1730, studied law at Edinburgh and Leyden, and travelled during 1741 in France and Holland.

[7][3] He spoke rarely, and attended irregularly, his principal interest lying in agricultural improvements.

He was appointed a Judge of the Court of Session on 3 June 1749, succeeding Robert Dundas of Arniston, and received the title of Lord Easdale.

Through his great-granddaughter, Emma Mure (1833–1911), who married Thomas Lister, 3rd Baron Ribblesdale (1828–1876), he was the great-great grandfather of Thomas Lister, 4th Baron Ribblesdale (1854–1925), who married the American heiress, Ava Lowle Willing (1868–1958), the former wife of John Jacob Astor IV (1864–1912).