In 1873, Plunkett was nominated as Secretary of Legation in Tokyo under Sir Harry Parkes. He left Tokyo in 1876 and served as Diplomatic Secretary in St Petersburg, Constantinople and Paris before being appointed Parkes's successor in Japan.
Plunkett was the British Minister in Tokyo, 1884–87, He was made a Knight Commander of the Order of St Michael and St George while in Tokyo.
In 1900 he was appointed Ambassador at Vienna. The following year he was appointed to the Privy Council in February 1901, and was created a Knight Grand Cross of the Order of the Bath (GCB) on 9 November 1901.