Hession's works have been performed internationally across Europe, America and Asia, in such venues as Westminster Abbey, King's College, Cambridge, St. John's (Smith Square), the Royal College of Music, and the Wellcome Collection, London and by ensembles including The King's Singers, Voces8, The Choir of Clare College, Cambridge, The Aurora Orchestra, the Manchester Camerata, the Commonwealth Festival Orchestra, Chetham's New Music Ensemble and Symphony Orchestra, the National Youth Chamber Choir of Great Britain, and Inner Voices. His works receive frequent broadcast on Classic FM and BBC Radio 3. He has recently completed a brand new commission from the Grammy-award-winning King's Singers, setting a text by Henry van Dyke entitled Master of Music; featured on their 50th Anniversary triple-disc, GOLD, the piece has received high praise in reviews from The Times and BBC Radio 3 Record Review. Other commissioners have included the Aurora Orchestra and Portsmouth High School.

In 2015, Toby was named a Senior Category Winner in the BBC Proms Inspire: Young Composers' Competition, for his setting of Christina Rossetti’s sonnet, After Death. His Recollections, for Violin and ‘Cello, was performed by members of the Aurora Orchestra at the Wellcome Collection, London, and broadcast live on BBC R3 during their ‘Why Music’ weekend residence in September 2015. The same year, he won the 18-and-under category of the 'A Carol for Christmas' competition, organised by the King's Singers, for his setting of Videntes Stellam; this was recorded by the National Youth Chamber Choir of Great Britain, and Inner Voices, and was broadcast on Classic FM on Christmas Day, 2015. More recently, Toby was named the winner of the inaugural Voces8 / VCM Foundation Composition Competition, with a setting of Lord Byron's She Walks in Beauty; in May 2018, he took first prize in the Flos Carmeli International Composition Competition, for his setting of the Maltese Marian antiphon text of the same name.