Directed by Blanche McIntyre, the piece sees Hickson return to the venue following her 2016 play Oil, which starred Anne-Marie Duff.
Garai's recent theatre credits include Queen Anne at the Theatre Royal Haymarket, Measure for Measure at the Young Vic, and The Village Bike at the Royal Court. Her film work includes Suffragette, Atonement and Nicholas Nickleby.
The Writer has design by Anna Fleischle, sound by Emma Laxton, lighting by Richard Howell, movement by Sasha Milavic Davies and casting by Julia Horan. Further cast is to be announced in due course.
Other productions in the Almeida's new season include Sophie Treadwell's Machinal directed by Natalie Abrahami (4 June to 21 July), Ontroerend Goed's £¥€$ (Lies) (31 July to 18 August), and the UK premiere of Clare Barron's Dance Nation (27 August to 6 October), directed by Bijan Sheibani.
The Writer runs at the Almeida from 24 April to 25 May, with previews from 14 April.