Donnelly made her on-screen debut in 2005 in the Channel 4 drama Sugar Rush. She is also known for appearing in Casualty, Hex, and as a main character in the Irish film Insatiable (2008). She also starred in Best: His Mother's Son, a BBC drama on the life of George Best, playing his sister Barbara.
She starred in Jez Butterworth's play, The River, at the Royal Court Theatre, alongside Dominic West and Miranda Raison. She reprised her role in the Broadway production alongside Hugh Jackman. In April 2018, she won the Best Actress award at the Olivier Awards for her performance in Butterworth's play The Ferryman.
Donnelly also participates in the featurettes "Introducing The Nevers," "A New Age of Power," "Character Portrait: Amalia True," "A Night at the Opera," "Confrontation and Translation," and "Telling Time."