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Molloy consolidated her stage reputation at both the Abbey and the Gate theatres, coming to Britain to tour with an Abbey production. She was invited to join the Royal Shakespeare Company and has played Gertrude to Kenneth Branagh's Hamlet in the West End.
In 1991 she was in the company that performed Brian Friel's Dancing at Lughnasa, about the sad lives of a group of sisters in pre-war rural Ireland, on Broadway, and was nominated for a Tony award, losing to co-star Bríd Brennan, although her role went to the Kathy Burke in the film version. She has appeared in such television plays and series, as Michael Palin's wife in the GBH and in New Tricks, Midsomer Murders, and Sex, the City and Me.
Among her theatrical credits are: Doubt: A Parable (Tricycle Theatre); In Celebration (Duke of York's Theatre); Dancing at Lughnasa, Juno and the Paycock, A Touch of the Poet (on Broadway); Juno and the Paycock (Donmar Warehouse); The Cripple of Inishmaan, On the Ledge, Hinterland (National Theatre); Arcadia (Haymarket); The Life of the World to Come (Almeida); The Hostage (Royal Shakespeare Company); and The Plough and the Stars (Young Vic).
She has appeared extensively in the plays of Irish playwright Brian Friel. On television, she has appeared in Waking the Dead, Foyle's War, Midsomer Murders, New Tricks, and the 1960s RTÉ soap opera Tolka Row.
She reprised her role for two episodes in 2015. Her film credits include Tara Road, The Blackwater Lightship and This Is the Sea. In April 2017, she will appear in The Ferryman at the Royal Court Theatre, ahead of a transfer to the Gielgud Theatre in the West End.