She was born in 1759 to an Irish father from Cork and an English mother from Liverpool. Her father was an apothecary, but he gave up medicine for the stage. As a girl, Farren was said to have beat a drum for his troupe of traveling players as they went from town to town.
After her father died, the family tried to support themselves with Elizabeth and her sister Peggy taking small roles on the stage. By the time she was 15, Elizabeth Farren was playing the role of Rosetta in Love in a Village, a ballad opera by Isaac Bickerstaffe and Thomas Arne.
In 1777, Farren appeared at the Haymarket Theatre in London as Kate Hardcastle in Oliver Goldsmith's She Stoops to Conquer. She lodged near the theatre with her mother. George Colman the Elder, who managed the Haymarket, allegedly gave her mother the nickname "Tin Pocket" after she gave her daughter a pocket lined with tin to hold hot boiled beef.
According to C.J. Hamilton, the turning point in Farren's career came when she was invited to perform at some private theatricals held by the Duke of Richmond. She acted together with the Earl of Derby, who was married at the time. Though the Earl was struck with Farren, she made a point of never being in his company unless in the presence of a third person for respectability's sake.
When Frances Abington retired in 1782, Farren took her place as the most prominent actress in London for depicting ladies of fashion. She played Mrs. Euston in Elizabeth Inchbald's comedy I'll Tell You What, and took on numerous Shakespearean roles, including Portia in The Merchant of Venice and Hermione in The Winter's Tale. All the while, Lord Derby followed her, now unhappily separated from his wife.
Lady Derby died in 1797, and the Earl proposed to Farren. She gave her farewell performance as Lady Teazle in Richard Brinsley Sheridan's A School for Scandal. She and Lord Derby had three children together, though only one daughter survived to adulthood.
Perhaps Farren's most famous legacy, though, was a portrait painted of her by Thomas Lawrence, now in the Metropolitan Museum of Art.