The Starks, Lannisters and Baratheons are featured very little in HBO's House of the Dragon, despite being the main focus of Game of Thrones. House of the Dragon aired its first episode on Sunday and will continue to air Sundays at 9PM Eastern for the remainder of its 10-episode season 1. The Starks, Lannisters, and Baratheons appear to be playing a very small role in this latest iteration of George R.R. Martin's world of A Song of Ice and Fire, but there's a reason why.
House of the Dragon centers around King Viserys I and who will succeed him on the Iron Throne. Before episode 1, at the Great Council of 101 AC (After the Conquest), Viserys was chosen to succeed his grandfather, King Jaeherys I. This set a precedent that the succession to the Iron Throne shall always go to a male and through the patriarchal line. Despite this precedent, Viserys names Rhaenyra, his firstborn daughter, as his heir. This was seen at the end of episode 1 and sets the stage for the upcoming civil war among the Targaryens that would later be known as The Dance of Dragons. Currently, the major houses of House of the Dragon are Targaryen, Velaryon, and Hightower.
While the Starks, Lannisters, and Baratheons are not expected to play a major role immediately in House of the Dragon, they will begin to appear more frequently as the series progresses. During the Great Council of 101 AC, Lord Ellard Stark supported Rhaenys, the Queen that Never Was, over Viserys. This was due in part to King Jaeherys forcing the Starks to give up land to the Night's Watch. This set the stage for whom the Starks would side with during the Dance of Dragons. The Baratheons also among the minority in supporting Rhaenys, while the Lannisters have long been allies with the Hightowers. This all sets up the factions and sides of the Dance of Dragons.
How The Starks & Lannisters Fit Into House Of The Dragon's Story
House of the Dragon will surely use multiple seasons to cover the entirety of the story that is the Dance of the Dragons, so it remains to be seen how soon the Starks, Lannisters, and Baratheons will begin to show up as major characters. During the upcoming civil war, the houses of Westeros must choose between Rhaenyra or Alicent Hightower, who later becomes wife to Viserys I. Lord Creggan Stark makes a pact to side with Rhaenyra, known as the Pact of Ice and Fire. He will support Rhaenyra's claim to the throne if someone of the royal family then weds a Stark in House of the Dragon. The Lannisters, led by twins Tyland and Jason, support the claim of Alicent Hightower and often hold office on the Small Council. The Baratheons originally support Rhaenyra, but when the Lord Boremund dies, his son Borros switches over support to Alicent.
These events are what make the great houses of Stark, Lannister, and Baratheon the major influences in the realm that they become during the events of Game of Thrones. If House of the Dragon sticks closely to the source material, then it may be a while until audiences see major characters from these houses in the show. It is inevitable that they will appear, however, as they are integral to the story and, of course, they also give a sense of familiarity to the viewer, connecting it back to Game of Thrones.