At the same time she was a part-time student at the Royal Scottish Academy of Music and Drama studying piano with Wight Henderson and viola with Frieda Peters.
She studied composition with Anthony Hedges and Robin Orr, and won the first BBC Scotland Young Composer’s prize in 1966.
In the late 1960s she spent three years at the University of Cambridge researching the operas of Sergei Prokofiev; she completed her PhD in 1970.
From 1969 she was a lecturer in the Faculty of Music at the University of Edinburgh, teaching composition, 20th-century history and analysis, and established the electronic and recording studios there.
McAllister edited the original version of Prokofiev's War and Peace which was premiered in Glasgow on 22 January 2010.