Wren attended Parsnips Youth Theatre in Harborough for four years. She was featured in the Mail in July 2006, when she and two others from Parsnips were chosen to be a part of the National Youth Theatre.
Wren started acting when she was talent spotted by Walt Disney UK at the age of 16. She was then engaged for Walt Disney's Comedy Sketch show Life Bites, playing the lead role as Chloe. She moved onto working with Nickelodeon in Genie In The House and Summer in Transylvania. In 2010 she appeared in Andrea Arnold's film adaptation of the classic novel Wuthering Heights, in which she plays Frances Earnshaw. In 2016 she plays Lady Evelyn Carnarvon in Guy Burt's tv mini-series Tutankhamun which is the story of the Archeologist Howard Carter, who discovered the tomb of Tutankhamun.
