The drama starring Pigott-Smith, who died earlier this month at age 70, airs May 14 on PBS.
The actor received Olivier and Tony award nominations for the London and New York runs of Mike Bartlett's play, which imagines the outcome after Charles inherits the British throne from his mother, Queen Elizabeth II. At 90, she is the nation's longest-reigning monarch.
Pigott-Smith already was a stage and screen veteran when he gained international attention as a sadistic police officer in British-controlled India in the 1980s miniseries "The Jewel in the Crown," which also aired on PBS.