Imrie's theatre credits include Acorn Antiques: The Musical (West End) and The School For Scandal (RSC). Her screen work includes Nanny Mcphee, Calendar Girls and Star Wars – The Phantom Menace
Clark has most recently been seen on stage at the Donmar in Les Liaisons Dangereuses. Other theatre credits include Romeo & Juliet (Crucible Theatre, Sheffield) and Violence & Son (Royal Court).
Tickets for Deborah Warner's production go on sale Tuesday 31 May.
King Lear opens at the Old Vic on 4 November 2016.