Game of Thrones ended in a way no one expected. For years, fans assumed the end would somehow involve a restoration of the Targaryen dynasty or at least a royal family being formed of some kind, and a next generation perhaps preparing to come along. Instead, democracy broke out. The end result was Bran Stark became king, with the idea that, since he can't have kids, when he died, a new king would be elected in his place. But did Tyrion miscalculate with this idea? Can Bran die? How long does the Three-Eyed Raven live?
It's an excellent question, considering what fans have seen on screen when it comes to the Three-Eyed Raven. Bran is led by his visions and Jojen beyond the Wall, up to a weirwood tree far to the north, where he discovers an incredibly wizened old man who is as much tree roots as he is a person. From all viewers are given to understand, Bran is supposed to study to become the next Three-Eyed Raven for decades under this guy, but is forced to take on the mantle early after the night king attacks the cave where they are hidden away.
Obviously, the original Three-Eyed Raven hadn't been planning on dying anytime soon. That's only the more incredible when one realizes he's already 125 years old and counting.
The TV show never bothers to delve into it, but in the fifth book in the A Song of Ice and Fire series, A Dance with Dragons, Bran pieces together who his mentor is. Called Lord Bloodraven, he was born in 175 AC, only 22 years after the death of the last dragon, and 21 years before the first Blackfyre Rebellion.
His name was Ser Brynden Rivers, bastard son of Aegon IV and Melissa Blackwood. Since his mother was highborn, he was treated well as a child and legitimized by his father by the age of nine. He was also an albino, and from an early age showed greenseer abilities, which almost certainly came from his Blackwood heritage. (The Blackwood crest is a giant weirwood covered in ravens. Sounds perfect for the Three-Eyed Raven to me!) Hence the name "Lord Bloodraven."
Brynden eventually went north to the Wall with Maester Aemon, as part of those who did not want to be used as pawns against Aegon V when he rose to the throne. He was elected Lord Commander before disappearing one day, never to be seen again.
When Bran meets Bloodraven in the year 300 AC, he's been the Three-Eyed Raven for at least 50 years and counting, having grown to be part of the tree he's been lying against the whole time, fed by the Children of the Forest and the tree sap. Now, if someone in his condition can live like that for decades upon decades, there is no reason that Bran should not be able to do so as well.
This doesn't make Bran immortal, mind you. However, it does mean he almost certain to outlive not just the highborn lords who elected him, but generations of his people. They will know no monarch who is not also the Three-Eyed Raven. Count Bran quietly make sure his successor is also a greenseer? Perhaps the Old Gods had a long-game plan to take back Westeros after all. Maybe they are the real winners of Game of Thrones.