Millar entered the Diplomatic Service in 1923, and served in various capacities at the British embassies in Berlin, Paris and Cairo and at the Foreign Office. From 1934 to 1938 he was Assistant Private Secretary to the Foreign Secretary (Sir John Simon, Sir Samuel Hoare and Anthony Eden respectively). During the Second World War he served chiefly at the British embassy in Washington, where he was also Minister Plenipotentiary from 1948 to 1950.
Millar was also the United Kingdom Deputy at the North Atlantic Council from 1950 to 1952 and its Representative thereon from 1952 to 1953.
The latter year Millar was appointed High Commissioner to the British Zone of occupied Germany, a post he held until 1955, and was then Ambassador to West Germany from 1955 to 1956. After his return to Britain he served as Permanent Under-Secretary at the Foreign Office from 1957 to 1962.
Millar was made a Knight Commander of the Order of Street Michael and Saint George in 1949 and a Knight Grand Cross of the Order of Street Michael and Street George in 1956, and in 1962 he was raised to the peerage as Baron Inchyra, of Street Madoes in the County of Perth. Lord Inchyra married in 1931 to Jonkvrouw Anna Judith Elisabeth de Marees van Swinderen (1906–1999), daughter of Jonkheer René de Marees van Swinderen, former Dutch Minister of Foreign Affairs (1908-1913) and Dutch Ambassador in London (1913-1937), of the Netherlands.
Their older daughter Elizabeth married Billy Wallace in 1965.
Their younger daughter, Dame Annabel Whitehead, was a Lady-in-Waiting to Princess Margaret and later to the Queen. Lord Inchyra died in October 1989, aged 89.