She studied viola at the Royal Northern College of Music, where she received composition lessons from Anthony Gilbert and Lennox Berkeley.
She later studied in Germany at the Hochschule für Musik Detmold, with the Italian violist Bruno Giuranna.
In 1994 and 1995 she co-hosted the Scottish Chamber Orchestra (SCO) composers' course in Hoy with Sir Peter Maxwell Davies.
Other works include three viola concerti, five string quartets, two percussion concerti (the second of which was written for Colin Currie with the Scottish Chamber Orchestra, Stanford Lively Arts and the Bergen Symphony Orchestra and premiered in 2012), and works for traditional instruments, including a concerto for clàrsach and fiddle concerto premiered by Catriona Mackay and Chris Stout in 2012.
In December 2010, it was announced that Beamish had been selected as one of twenty composers to participate in the New Music 20x12 project as part of the London 2012 Cultural Olympiad.
[5] In March 2016, Beamish was elected a Fellow of the Royal Society of Edinburgh, Scotland's National Academy for science and the arts.
Beamish was appointed Officer of the Order of the British Empire (OBE) in the 2020 Birthday Honours for services to music.