Although House Stark is one of the most important great houses in "Game of Thrones," they're much less significant in the era depicted in "House of the Dragon." In "Fire and Blood," House Stark is mostly in the background during the Dance of the Dragons, the Targaryen civil war that the new TV show will focus on. The Starks side with Rhaenyra Targaryen, although they're not in the thick of the war. However, Cregan Stark, the Lord of Winterfell, serves an extremely brief tenure as Hand of the King for one of the last Targaryen heirs.
In episode one, Lord Rickon Stark is seen pledging loyalty to the throne and to Rhaenyra as heir. Rickon is Cregan's father.