The story of House of the Dragon will be able to add to Game of Thrones, including greater explanation of one key location. House of the Dragon's timeline takes place around 200 years before Game of Thrones, beginning in 101 AC, with the Targaryen civil war at its center, the Dance of the Dragons, running from 129-131 AC. In contrast, the story of Jon Snow, Daenerys Targaryen et al starts around 298 AC. That means it will be a very different Westeros, with some families missing (the Martells and the Tyrells have no real role to play in this story), others different (the Starks won't be the main heroes), and some new ones added in (like House Velaryon).
In terms of Game of Thrones' Westeros locations, House of the Dragon will revisit some of the most important places, as well as introducing new ones. Viewers can be expected to become familiar with somewhere like Driftmark, the family home of House Velaryon, but there'll also be plenty of locations seen in the parent show. These include the great, burned castle of Harrenhal, the Targaryen ancestral home of Dragonstone, and various parts of King's Landing, including the Dragonpit that sits Rhaenys' Hill.
The Dragonpit in Game of Thrones became incredibly important, but only as a place where key meetings and decisions were made. It's here where the Westerosi nobles gather for their summit in season 7 to try and take decisive action in the war against the Army of the Dead, and where the Great Council is held to elect Bran Stark as King in Game of Thrones season 8. But even a minor background character in Game of Thrones refers to it as a "damned ruin," which is very much not the case in the prequel. House of the Dragon will have 17 dragons, many of which will be held in the Dragonpit, meaning viewers will be able to see it operational for its original purpose. Rather than just an old ruin, this will be (based on the trailers) more like a giant temple, one crucial to the story of the dragons, and to the civil war, meaning there'll be a much clearer sense of its importance and history than Game of Thrones.
How The Dragonpit Fits In House Of The Dragon's Story
Though important in Game of Thrones, the Dragonpit will feature even more prominently within House of the Dragon's story, a lot of which is centered around King's Landing and sees some critical events occur at the location. It became much more than just a place to house dragons, but was even home to coronations - it's where Aegon II Targaryen, one of the two claimants to the Iron Throne, was crowned King; when his half-sister Rhaenyra Targaryen took the city, she held executions there - it is a monument to both of their failures. Biggest of all is an event that comes during the latter's time in the city, known as the Storming of the Dragonpit, which, as the name suggests, saw thousands of people rise up against the ruler and storm the Dragonpit, killing the five dragons inside (though not without considerable loss of human life as well).
That particular event helped turn the once great Dragonpit into ruins; though restoration attempts were later made, various other issues - including a great sickness shortly after the Dance of the Dragons, which resulted in bodies having to be piled into the Dragonpit and burned - meant it was never truly restored to its old glory, explaining the location as-seen in Game of Thrones. The Dragonpit should prove fascinating (if also disturbing at times) in House of the Dragon for how it showcases different sides to the dragons, seeing more of a place they are kept to, how they respond and the impact upon them, and of how they can be killed by smallfolk. The Dragonpit in House of the Dragon and Game of Thrones is similar to the fall of the Targaryen dynasty itself, once the great home of dragons, reduced to a few remaining ruins.