The King of Ingary is the leader of the kingdom of Ingary, as his name suggests. There is only one King during the course of the story, and he is never named. He is the elder brother of Prince Justin and father to Princess Valeria in the books.
The father of the current King of Ingary was the one to banish the Witch of the Waste to The Waste.
Plot
Novels
The King appears when Sophie enters the palace in Kingsbury, to talk to him while pretending to be Howl's mother about Howl. He also mentions that Strangia and High Norland will declare war on Ingary and needs his brother back, since his brother went to the Waste to look for the missing Wizard Suliman and is a general. He also summons his daughter, Valeria when Sophie comes back to the palace. He also makes Howl a Royal Wizard when Sophie suggests it.
The King has a small part at the end of the book, where he promotes Abdullah and Flower-in-the-Night to Ambassadors.
Film
The King is mentioned several times in the film. Howl also receives a message from the King about the war. Howl comes in disguise as the King, while Sophie (disguise as Howl's mother) is talking to Suliman. Howl get exposed as the real king comes in.