The daughter of a magazine editor and a surgeon Kirby was turned down by Bristol Old Vic Theatre School and took a gap year travelling before studying English at Exeter University. She then turned down her place at LAMDA in London after she was signed up to an agency and met the theatre director David Thacker who gave her three starring roles over 2009 at the Octagon Theatre Bolton in All My Sons by Arthur Miller, Ghosts by Henrik Ibsen and A Midsummer Night's Dream by William Shakespeare. For All My Sons she won the BIZA Rising Star Award at the Manchester Evening News Theatre Awards, worth £5000.
She then went on to star at the National Theatre as Isabella in Women Beware Women by Thomas Middleton directed by Marianne Elliott alongside Harriet Walter and Harry Potter's Harry Melling. She then starred as Rosalind in As You Like It by William Shakespeare at the West Yorkshire Playhouse in Leeds, where Alfred Hickling from The Guardian named her a "significant new talent". In 2011 she was in premiere of The Acid Test by Anya Reiss at the Royal Court Theatre directed by Simon Godwin earning praise for her performance with Paul Taylor of The Independent calling her "a star if ever I saw one".
She has been nominated for the Ian Charleson Award for two consecutive years for five out of the six plays, 2010 and in 2011, where she won Third Prize, Ben Whishaw and Benedict Cumberbatch being previous winners.
Her TV debut in the BBC's The Hour co-starring with Ben Whishaw, Dominic West and Romola Garai aired in 2011. She played Estella in the BBC's adaption of Great Expectations. alongside Ray Winstone, Gillian Anderson and Douglas Booth.
In 2011, she was named as one of Screen International 'Stars of Tomorrow'. Previous names include Gemma Arterton, James MacAvoy and Carey Mulligan. In November, she was nominated for the Evening Standard Theatre Awards as Outstanding Newcomer for her performance in The Acid Test. Named as one of Nylon's Young Hollywood list 2012.
She is set to star as the lead role of Alice in Ridley Scott's forthcoming mini-series adaptation of Kate Mosse's novel Labyrinth.
Filmed Wasteland alongside Luke Treadaway and Timothy Spall in early 2012, and The Necessary Death of Charlie Countryman with Shia Leboeuf and Mads Mikkelson.
She is filming Richard Curtis' next film About Time] with Rachel McAdams, and played Masha in Three Sisters at the Young Vic in September.[