HBO has multiple Game of Thrones spinoffs coming. According to Deadline, production has officially begun on the first of them, a prequel series called House of the Dragon. The show tells the story of Targaryen 300 years before the events we saw in Game of Thrones.
The cast features Paddy Considine as King Viserys Targaryen, Olivia Cooke as Alicent Hightower, Rhys Ifans as Otto Hightower, Emma D’Arcy as Princess Rhaenyra Targaryen, Matt Smith as Prince Daemon Targaryen, and Steve Toussaint as Lord Corlys Velaryon, AKA the Sea Snake, a character who later becomes Hand to Queen Rhaenyra Targaryen according to the history established in George R.R. Martin's A Song of Ice and Fire books.
The series is being shot right now and is expected to premiere sometime next year.