The dragon Balerion is known as the Black Dread, and with good reason. One of the most significant dragons in "Fire and Blood," he's ridden by Aegon I during the Targaryen conquest of Westeros. He is also ridden by other Targaryen descendants over the course of his long life. Unlike many of the other dragons in the book, he lives out a long life, dying of old age during the reign of Jaehaerys I long before the civil war.
"House of the Dragon" is currently poised to cover the civil-war era, so unless there are flashbacks, we probably won't see Balerion depicted on screen.