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Stark began his career in music as a principal violinist. He trained in conducting at the Royal College of Music with Norman Del Mar and in Vienna with Sir Charles Mackerras. He is currently a professor of conducting at the Royal College of Music and Rehearsal Director of the European Union Youth Orchestra.
During his career, he has conducted orchestras such as the London Symphony Orchestra, the Malaysian Philharmonic Orchestra, the Orchestra of the Age of Enlightenment, Hallé, Bournemouth Symphony Orchestra, BBC National Orchestra of Wales and the English Chamber Orchestra, and has worked alongside Pierre Boulez, Sir Colin Davis, Sir Mark Elder, Bernard Haitink, Lord Menuhin, Sir Roger Norrington and Klaus Tennstedt.
Stark has made his career in music education. In addition to his work with the European Union Youth Orchestra he was Conductor-in-Residence for the National Youth Orchestra of Great Britain for 25 years. He is Principal Conductor of the Arabian Youth Orchestra and also conducts orchestras ranging from the Hertfordshire County Youth Orchestra (principal conductor since 1994) to the New South Wales Youth Orchestra of Australia and the Derbyshire City and County Youth Orchestra.