After studies with Peter Sculthorpe (1965–69) in Australia and with Toru Takemitsu (1970) in Japan, Barry established himself in the following decades as one of Australia’s international composers, with premieres and performances of his works in Japan, North and South America, Europe, the UK and at home. Notable premieres in the last few years have been in Palma, Hong Kong, Boston, Brisbane, Sydney, Melbourne, Tokyo, Vienna, and St Petersburg.

Over his career he has published almost 100 works (Universal Edition and Hal Leonard) and released over 60 recordings and videos, including those by the London, Netherlands Radio, New Zealand, and all Australian Orchestras, as well as ensembles and soloists from Poland, Japan, the UK, Europe, Russia, America and Australia.

In 2016 he was appointed Redmond Barry Distinguished Professor of Music at the University of Melbourne. In 2021 Conyngham returned to full-time composition.