Game Of Thrones: 9 Early Predictions For Season 7
6. Sam Will Discover Some Key Knowledge
Despite leaving in Season 5, Sam didn't arrive in Oldtown until the end of Season 6. Sure, his storyline wasn't all that interesting, and he only appeared in three episodes, but it was probably the only arc to actually have a realistic sense of travelling and time so it's no doubt very popular with everyone who complained about Varys in the finale.
With there being just two seasons and roughly 13 episodes left, it'd take some of those timey-wimey plot shenanigans for Sam to actually become a Maester - there's no way he can really do that given how long is left. That means he has to quickly serve his purpose and get out of there, and that means discovering some key information about the White Walkers.
It's not yet clear what it'll be, although a believable theory is that it'll be the secret to making Valyrian steel and/or dragonglass, in order for the realm to forge enough weapons to defend themselves against the coming army.