Tyrion (played by Peter Dinklage) is one of the most beloved characters in Westeros, where he currently serves as Hand of the Queen to Daenerys Targaryen (Emilia Clarke). The so-called "Half-Man" has given up everything in support of his chosen queen, and he has proven himself to be an ally of Jon Snow (Kit Harington) as well. However, fans still see plenty of room for him to turn on his liege lords.
For plausible fan theories, look no further than the Season 7 finale. At the time, Daenerys had pledged to help Jon Snow in his war against the White Walkers. The only thing left to do was ensure that Cersei Lannister (Lena Headey) could not sneak up on them from the south and take them unaware, sandwiched between two hostile armies. They held a great council where they requested a ceasefire until the undead threat had been dealt with.
As fans know, Cersei refused at first, returning to her chambers in anger. However, Tyrion approached her alone to try and persuade her. The show included only part of the siblings' conversation, right up until the point that Tyrion guessed that Cersei was pregnant. After that, they returned to the dragon pit where Cersei announced that she would help in the war for the dawn.
What passed between them here is a mystery that many fans have tried to unravel. A fan theory proposed by Reddit user Enervata makes the case that Tyrion promised Cersei the ultimate security for her unborn child: the throne. In Season 7, Tyrion was deeply concerned with the fact that Daenerys said she could not have any children. Perhaps thinking that there would be no rightful heir anyway, Tyrion promised to legitimize his nephew in the role in order to get Cersei's help against the White Walkers.
Fans can argue about whether this constitutes a "betrayal" of Daenerys, although she herself will likely see it as such. The Dragon Queen believes she was cursed to be sterile by the witch Mirri Maz Durr, who also promised her three betrayals in her life -- "once for blood and once for gold and once for love." The first was likely Mirri herself, while the second seems to have been Jorah Mormont, who spied on her for Varys. The third is up for debate, but some fans think Tyrion will "betray" her for love of both her and his family, in an attempt to keep them from fighting.
The most glaring flaw in this theory is Cersei's double-cross. As soon as Daenerys and Jon leave King's Landing, she reveals that she is not sending her armies north as promised. She intends to take on whatever surviving threat makes its way south -- be it the White Walkers or the surviving humans. Obviously, she could not count on Tyrion honoring his part of the bargain if she did not do the same.