In the Game of Thrones universe, treason is generally punishable by death. The methods vary, but more often than not, standing against the crown will result in you being violently separated from your head. However, there is a slight caveat to that rule. Treason is really a matter of perspective, so if one's illegitimate acts are in line with the whims of power, they aren't actually treasonous; at the very least, these actions won't earn them a spot on the executioner's block.
When nefarious plots that fly in the face of tradition and royal law are carried out by royals themselves, it's especially difficult to hold anyone accountable for their actions. In House of the Dragon, Following the death of King Viserys, it was revealed that Queen Alicent and her father, Ser Otto Hightower, along with a handful of the most powerful non-Targaryen individuals in Westeros, a political faction called the Greens, had long been plotting to install Aegon, the Queen's firstborn son, as king, which is a direct affront to the late King's wishes.
Audiences have long suspected that the Greens would go this route, as there are a lot of questions surrounding the legitimacy of the King's chosen Successor, Princess Rhaenyra, and the parentage of her three children, who would ultimately ascend to the throne. There was no one powerful enough in King's Landing to challenge their claim, and the end of "The Green Council" saw Aegon being crowned in front of a packed Dragonpit.
Princess Rhaenyra Won't Take the Ascension Lying Down
At the moment, there seems to be a consensus (or, at the very least, a general fear among the common people about challenging the status quo) at King's Landing that King Viserys genuinely amended his wishes for his succession and chose Aegon to take the Iron Throne. However, Princess Rhaneyra was his chosen successor, so those who still hold loyalty to the rightful heir will certainly challenge Aegon's ascension.
Princess Rhaneyra holds no love for Queen Alicent and is well aware that a treasonous plot to deny her taking power was possible. As of yet, it's unclear who will stand by her side in the upcoming conflict, but at the very least, Princess Rhaenyra and her uncle/husband, Prince Daemon, both formidable dragonriders, will be a massive thorn in the side of Aegon's new Kingdom.
House Targaryen has ruled Westeros for hundreds of years. The show promises to tell the story of their fall from power. This conflict promises to be a bloody mess, and it's easy to imagine how the Kingdom will descend into chaos as the Greens and Blacks vie for the Throne.
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House of the Dragon, as the name suggests, features quite a few dragons. Now that the most powerful families in the Kingdom will need to choose sides, and House Targaryen seems to be split in two, who controls said dragons will be of the utmost importance. In Game of Thrones, Daenerys Targaryen managed to raze King's Landing with a single dragon.
At the beginning of House of the Dragon, it was revealed that House Targaryen currently has 17 dragons, though only a handful is fully grown. It seems as if both sides of the impending conflict will have a handful of dragons, though the Blacks may have a slight advantage in that department. The end of "The Green Council" already saw Rhaenys smashing through the floor of the Dragonpit and threatening to burn the treasonous Greens before their plot ever got off the ground.
Dragons are an essential implement in war, and those who ride them into battle will define the future of the Kingdom.
Civil War Will Soon Rock Westeros 
It seems inevitable that civil war will soon break out in Westeros. It will essentially be a family feud, though the Hightowers seem to be at the center of the traitorous usurpation. Powerful Westerosi houses will need to choose sides in the war to come. Who will stand behind the illegitimate King Aegon, and who will support the controversial claim of Princess Rhaenyra?
Only one episode remains in House of the Dragon's debut season. It will be titled "The Black Queen," which is likely a reference to Princess Rhaenyra and the loyal army she will amass to confront Queen Alicent and the Greens. The upcoming civil war will be the defining characteristic of upcoming seasons. As the events of Game of Thrones took place directly after House Targaryen was stripped of their power, one can speculate that the Blacks will come out on top of the conflict, allowing the family to maintain their solitary claim to the throne.
It will be fascinating to see how the war plays out and who survives to tell the tale.