Þórunn Gréta studied composition at Reykjavík College of Music and completed a pre-diploma in composition in 2008, B.A. in composition at Iceland Academy of the Arts in 2011 and M.Mus. at Hochschule für Musik und Theater Hamburg in 2014. Her composition teachers were Úlfar Ingi Haraldsson, Atli Ingólfsson and Manfred Stahnke. She was an active participant at Internationale Ferienkurse für Neue Musik Darmstadt in 2012 attending Master Classes with Brian Ferneyhough, Georges Aperghis and more.
Her music has been performed by various ensembles and soloists, such as Caput Ensemble, Cikada Ensemble, Skark Ensemble, Duo Harpverk, Kristinn Sigmundsson, Hanna Dóra Sturludóttir, Elisabeth Holmertz and the Icelandic Symphony Orchestra.
In her most recent works she has been experimenting with the form of contemporary music theatre and music in relation to text and phonetics as well as composing soundscape to theatre performances, vocal music and chamber music.