Elder was 1979-1993 Music Director of English National Opera. He also worked from 1989 to 1994 as Music Director of the Rochester Philharmonic Orchestra in the United States from 1992 to 1995 as Principal Guest Conductor of the City of Birmingham Symphony Orchestra and the BBC Symphony Orchestra (1982-1985) and the London Mozart Players ( 1980-1985 ). Since 2000 he has been chief conductor of the Hallé Orchestra in Manchester.
Elder worked with internationally renowned orchestras as the Chicago Symphony Orchestra, Boston Symphony Orchestra, the Royal Concertgebouw Orchestra Amsterdam, the Los Angeles Philharmonic Orchestra and the Orchestre de Paris and has conducted at opera houses such as the Royal Opera House Covent Garden in London, the Metropolitan Opera New York, the Opéra National de Paris, Lyric Opera of Chicago, Glyndebourne Festival Opera and the Bavarian State Opera in Munich. He was also guest conductor at the Bayreuth Festival and is a regular contributor at the Proms with.
He was awarded the Order of the British Empire, 1991 with the Olivier Award in 1989. In 2008 he was knighted.
In 1980, he appeared as one of the first western conductors in East Berlin and the conductor for the world premiere of Friedrich Goldmann's Violin Concerto at the Komische Oper.