According to co-star Timothée Chalamet’s agent, Brian Swardstrom:
The release date is not set yet.
— Brian Swardstrom (@brianswardstrom) January 4, 2019
According to Vulture,
The King (June 22)
Timothée Chalamet. Robert Pattinson. A “little frilly frock.” The King, based on Shakespeare’s Henry the IV and V, is the first movie conjured entirely by stan Twitter — and that’s not even mentioning the hair! Chalamet plays Henry V, who’s navigating life on the throne. Scripted by Joel Edgerton and David Michôd, and directed by Michôd, it also features Sean Harris, Ben Mendelsohn, and Chalamet’s maybe girlfriend Lily-Rose Depp. (Please respect my privacy at this difficult time.) Pattinson is Henry’s glamorous frenemy, King Charles VI of France’s son, called “The Dauphin.”