Dervla was born in October 1971 in Churchtown, Dublin, Ireland.
Her first credited TV roles were in the TV series Troubles in 1988 and The Lilac Bus in 1990 alongside Stephanie Beacham based on Maeve Binchy's novel.
She got her television break in the 1991 BBC Scotland production of A Time To Dance, adapted by Melvyn Bragg from his own novel, playing Bernadette Kennedy.
For 23 episodes, from 1996–1998, she appeared in Ballykissangel in the role of Assumpta Fitzgerald. She also continued this role for a Comic Relief special of The Vicar of Dibley, and in a Father Ted special. Dervla 's performance in Ballykissangel won her the National TV Award for Best Actress in 1996, and the Irish Post Award for Best Irish Entertainer in 1997.
More recently Dervla appeared in the four-part BBC drama The Silence in 2010. For her role as Maggie, Dervla won the Dagger for Best Supporting Actress at the 2010 Crime Thriller Awards.
In April 2013, Dervla was cast as Valerie in Josie Rourke's revival of The Weir by Conor McPherson at the Donmar Warehouse. Dervla appeared alongside Brian Cox, Ardal O'Hanlon, Risteard Cooper and Peter McDonald.
Dervla is married to actor Rupert Penry-Jones, with whom she has two children, Florence and Peter.