Currently, the Game of Thrones universe is defined by Targaryen family. House of the Dragon follows the Dance of the Dragons succession battle between Rhaenyra Targaryen and Aegon II. A Knight of the Seven Kingdoms follows Rhaenyra's great-great-great-great-great-grandson Maekar and his sons Aerion and Aegon, and then Game of Thrones picks up with Aegon's great-granddaughter Daenerys. However, that's not the only family connection between the different shows.
The most important thing for you to know is that by the time Ser Duncan rides into Ashford Meadow at the start of this series, the people of Westeros have grown tired of the Targaryens. A Knight of the Seven Kingdoms is set over 200 years into the Targaryen dynasty, and about 70 years after the devastating civil war depicted in House of the Dragon.