She studied at Queen"s University Belfast where, at the age of twenty, she began to compose.
Further studies were in London and in Denmark (the latter with Per Nørgård). Subsequent major works have included the piano quartet Jack B. (inspired by the work of the Irish painter Jack B Yeats), the piano trio How to Make the Water Sound, the opera Hey Persephone!, the violin concerto Venus Blazing and the clarinet concerto Celestial Pied Piper, the latter composed in New York where she was a Fulbright Fellow in 1999-2000. She was Artistic Director of the London-based Society for the Promotion of New Music (SPNM) from 2003-2005.
Richard Morrison of the Times wrote of her in June 2004: "This Belfast born composer is one of the most original thinkers in years."
Gribbin lectures in composition at Trinity College of Music in Greenwich.