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Hickson's first play, Eight, produced by the Edinburgh University Theatre Company, won a Fringe First, the Carol Tambor Best of Edinburgh Award and the NSDF Emerging Artists Award at the Edinburgh Fringe in 2008. The show toured to New York City in January 2009 and opened at Trafalgar Studios in July 2009.
In 2013 her play Wendy & Peter Pan, an adaptation of J.M. Barrie's novel, was produced at the Royal Shakespeare Company for the Christmas 2013 season, directed by Jonathan Munby. It was later revived for the Christmas 2015 season.
In 2019 Anna a binaural thriller, opened at The National Theatre. Hickson collaborated with sound designers, Ben and Max Ringham. The play was directed by Natalie Abrahami. 
Hickson currently teaches at Oxford University.
Hickson is the youngest person ever to be published by Nick Hern Books.
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- Taylor, Paul (25 April 2018). "The Writer, review: Unflaggingly provocative". The Independent. Retrieved 20 May 2018. CS1 maint: discouraged parameter (link)
- Flood, Alison (28 June 2018). "Royal Society of Literature admits 40 new fellows to address historical biases". the Guardian. Retrieved 3 July 2018.