The model will star in a one-off episode called Timeless, which tells the story of two women who have been torn apart from their lovers during the war.
Cara, 21, will be acting in the short drama, which is due to air in May, alongside veteran actress Sylvia Syms.
Written by Tim Firth and directed by Tony Smith, Timeless is described as an "engaging tale of love, loss and hope".
The synopsis reads: "Alice and Chloe may be generations apart but both share the pain of having been separated from their partners by war. Chloe's soldier fiancé is serving a term of duty in Afghanistan when an army official arrives at Alice's door. The two women are shocked by the news but the generation gap is finally closing."
Other stars who have signed up for the new Playhouse Presents series - which consists of eight 30 minute one-off plays - include Matthew Perry, Jo Brand, Billie Piper and Ashley Walters.
Cara dabbled in acting in 2012 with a minor role in Anna Karenina. She also has a forthcoming appearance in The Face of an Angel, which is based on the Amanda Knox murder case.
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