The Others

Jaime is the twin brother to Cersei, and if Cersei were to die, he would certainly be close enough to the throne to take over control.

Sansa is an outsider, but her leadership in the North, and time spent in King's Landing give her an advantage in taking over control of the realm.

Bran has given up his claim to Winterfell, but he still could take the throne if his visions guided him to do so. Bran is able to see the past, present, and future, which gives him some obvious advantages.

Arya is strong, cunning, and determined. She could easily beat anyone in combat, and could work her way into the throne room if she desired.

Gendry is a bastard son to King Baratheon. He held a more legitimate claim to the throne than Cersei's bastard children, and he is in a good position to take control of the destiny of the realm.

The Hound hates everything about Kings. This makes him an unusual pick for someone to rule, but he is strong, smart, and would be able to do it if he had to.

Ned Stark started the search for the rightful heir to the throne. Who will stake the claim and who will die trying? Season 8 will be out soon enough, and until then any character could be the next in line.