In the original Game of Thrones series, countless individuals sat on the Iron Throne at one point or another. Almost all of them wound up dead, be it from a rogue, rampaging boar, poisoned wine, or suicide. Once a person finds themselves in power, it can be incredibly difficult to maintain their position, especially in turbulent political times.
House of the Dragon tells the tale of House Targaryen's decline. Fans of the original show will recognize this family as having spawned Daenerys Targaryen, one of the series' primary protagonists (and, ultimately, its most fearsome antagonist). Much like its predecessor, this new spinoff has already proven to be fraught with intense political struggles. Everyone in the halls of power has lofty ambitions and will stop at nothing to see themselves ascend to the highest possible position. In all likelihood, many will have the opportunity to control Westeros throughout the course of the series.
Audiences already understand that this show will depict House Targaryen's death, which probably means that internal turmoil proved catastrophic for the family. In the end, only one person can win the game of thrones. Who will it be?
The Current Ruler of Westeros, King Viserys I Targaryen 
During the first few House of Dragon episodes, the man sitting in the coveted metal chair has been King Viserys I Targaryen. Though his family, with a horde of dragons at their backs, have ruled Westeros for an incredibly long time, he doesn't seem all that qualified for his position. He lacks the sturdy constitution that generally characterizes kings and queens and appears to make decisions based on his own flights of fancy rather than rational geopolitical considerations.
It's possible, albeit unlikely, that King Viserys could maintain his position throughout House of the Dragon. However, given the fact that the character has already shown signs of a degenerative disease, his days are likely numbered, and his death is sure to set off a major conflict.
Princess Rhaenyra, the King's Appointed Heir 
After his first wife died in childbirth, followed quickly by his newborn son, King Viserys was forced to choose an heir. He chose his daughter, Princess Rhaenyra, in a decision that aggravated many powerful individuals. Selecting a woman as a successor broke with years of tradition for the royal family, and as such, it's safe to assume that there will be some complications if the Princess ever needs to become the Queen.
Whether or not Rhaenyra will be the immediate successor to King Viserys is as of yet unclear. However, she is a powerful dragonrider, so if there is disagreement about her ascension, she will surely cause problems for those who reject her claim to the throne.
Prince Daemon Targaryen, a Scorned Brother With Lofty Ambitions .jpg)
When King Viserys announced his heir, many assumed it would be his brother, Daemon Targaryen. However, given the fact that Daemon had long been a thorn in the King's side, he ultimately opted against it.
Early in the season, it seemed as if Daemon would be an antagonist in the series. However, he has since reclaimed the Stepstones for the Kingdom. In the most recent episode, he had a sultry dalliance with Princess Rhaenyra before asking his brother to marry them, as incestuous partnerships to secure the royal bloodline are common in House Targaryen. Daemon is a formidable warrior, and his status would be elevated even further if he were to marry Rhaenyra. These facts could make him a strong contender to eventually take the Iron Throne.
Aegon Targaryen, King Viserys' Firstborn Son, and the Heir Apparent
Princess Rhaenyra's status as heir was threatened when King Viserys had a child with his new wife, Alicent Hightower. Their newborn baby Aegon is King Viserys's first male child, which would generally mean he is next in line for the Iron Throne. Obviously, Aegon has a lot of growing up to do before he can rule Westeros. However, as the series will eventually jump forward in time, he may supersede Rhaenyra's claim.
House of the Dragon is based on the same fantasy novels as Game of Thrones, George R.R. Martin's A Song of Ice and Fire saga, so it's likely that many of those who have been a fan of the story since it was simply words on paper already know where the series it headed. Nevertheless, it is almost impossible to predict what might happen next for those who are watching the show without prior knowledge. King Viserys seems to be in the process of dying, and who will be his heir is a mystery. It's easy for fans to theorize all manner of chaos that could come about from the impending power vacuum.
The Iron Throne will be hotly contested, and that is not just a reference to fire-breathing dragons.