Her first acting roles were at the Abbey Theatre in Dublin. In 1975, she moved to London and joined the Royal Shakespeare Company starring in Dion Boucicault's London Assurance in the West End. Cusack's work with the Royal Shakespeare Company continued with an award-winning performance as Celia in As You Like It which included the Clarence Derwent Award and her first Olivier Award nomination. She secured a second Olivier Award nomination for her performance in The Maid's Tragedy by Francis Beaumont and John Fletcher in 1981, followed two years later with a third Olivier Award nomination as Kate in The Taming of the Shrew. She made her Broadway debut in 1984 performing in repertory with the Royal Shakespeare Company. Starring opposite Derek Jacobi, she played Roxane in Anthony Burgess' translation of Edmond Rostand's Cyrano de Bergerac and Beatrice in william Shakespeare's Much Ado About Nothing, directed by Terry Hands. The production of Cyrano de Bergerac was later filmed in 1985. Much Ado was first produced at the Royal Shakespeare Theatre in Stratford-upon-Avon in 1982–83, then moved to London's Barbican Theatre for the 1983–1984 season where it was joined by Cyrano, before both plays came to New York's Gershwin Theatre from October 1984 to January 1985, for which Cusack received a Tony Award nomination for her performance as Beatrice, and costar Jacobi won the award for his Benedick. During this period, Cusack and her husband, Jeremy Irons, appeared in a "Shakespeare Winter's Eve", a major fundraiser for the Riverside Shakespeare Company in New York, along with other members of the Royal Shakespeare Company. Following the Broadway run, the plays toured the US, making stops in Washington DC and Los Angeles. Cusack's relationship with the Royal Shakespeare Company continued with a series of leading roles include Portia in The Merchant of Venice opposite David Suchet, Lady Macbeth opposite Jonathan Pryce in Macbeth and Cleopatra in Antony and Cleopatra in Stratford upon Avon and at London's Haymarket Theatre in the West End.