[1][2] As well as holding the Earldom of Dunmore, Murray is also the Viscount of Fincastle and Lord of Blair, Moulin and Tillimet.
[2] In 1998, he visited his ancestral home in Airth to plant a memorial tree beside the Dunmore Pineapple.
Murray studied at Launceston College, Tasmania and later worked as an Electrical Technical Officer for Airservices Australia.
[2] Dunmore is the Patron of the Scottish Australian Heritage Council, Crown International Dance Association, Australia Day Council (Victoria), The Company of Armigers Australia, The Armorial & Heraldry Society of Australia, Tasmanian Caledonian Council, The Murray Clan of Victoria, The Murray Clan of New Zealand, St Andrew's Society Tasmania, Tullibardine Pipe Band NSW, Co-Patron of St Andrew's First Aid Australia, The Murray Clan of Edinburgh, The Murray Clan Society of North America, Honorary member of the Murray Clan of NSW.
Dunmore being the first peer of the realm to be installed as the foundation Worshipful Master of a Masonic lodge consecretated in the name of a peerage.