Jon Snow is a man with a plan, and that plan is to kill the Night King on Game of Thrones. He thinks that, by killing the wight and White Walkers' creator, it will destroy the whole army. But who is actually going to carry out this plan? Will Bran kill the Night King? Right now the plan seems to be to let Bran be the bait, and then let someone else kill the Night King. Bran may have the world's knowledge, but he's not nearly as skilled in combat as the Night King is.
Jon seems to want to use dragon fire to kill the King, although it's unclear if that will work. Jon said he wanted to have the dragons nearby, protecting Bran, for when the King comes. "We need to be near [Bran]. Not too near, or the Night King won't come. But close enough to pursue him when he does," Jon said. "Dragon fire will stop him?" asked Arya. "I don't know. No one's ever tried," Bran said. Jon may be the first to try if this plan succeeds. But there are about 100 different ways it could go wrong. The King could sense that it's a trap and not show up at all. Or, he could kill everyone including the dragons if the dragon fire doesn't work.
However, there are a couple of other possibilities. According to Vox, there's a theory that Bran is the Night King, and he became trapped in the King's body when he spent too long warging into him to try to stop him from becoming the Night King in the first place. Fans saw with Hodor how much damage can be done with Bran trying to change the past and staying in visions for too long. Perhaps the only way to kill the Night King now is for Bran to sacrifice himself. That could be what his ultimate plan is.
One other possibility is that Bran will usurp Jon's plan to kill the Night King by doing it himself. Bran said he'd be waiting for the Night King in the Godswood. Now, it's worth noting that the Godswood at Winterfell has a Weirwood tree. Bran saw the Night King's creation in one of his visions. He knows that the King was a man who was pinned to a Weirwood tree by the Children of the Forest who stabbed him with a Dragonglass spike. Perhaps Bran is trying to kill the Night King the same way, therefore undoing the magic making him the King who controls the army. Bran is going to be waiting for him under the Weirwood. If he can somehow get close the King to come close enough, Bran can draw a secret Dragonglass knife and take the King by surprise to stab him through to the tree.
We haven't seen Bran fight much in this series after his Season 1 accident, but he may have it in him to carry out this act. No one else knows the King's origin story, but Bran is armed with that knowledge that may also be the King's undoing. But... Bran may also die attempting it and Jon and co. will be back to square one. Fans will have to wait to see, but it would be awfully poetic for the King to die the same way he was created and at the hands of the Three-Eyed-Raven.