It won't happen straight away, but at some point next season we believe all the remaining Starks will be together again. Jon and Sansa have already been reunited, Bran is now back at the Wall, and Arya has already returned to Westeros — all the pieces are coming together.
We think Sansa's increased levels of badassery will combine with her frustration over Jon getting all the credit for defeating Ramsay in the Battle of the Bastards (despite the fact he'd definitely have lost if it wasn't for her) and lead to her doing something reckless.
It's less likely, but the other possibility is that she might go completely rogue. We know from George R. R. Martin's 1993 letter to his agent detailing the initial outline for A Song of Ice and Fire that he'd originally intended for Sansa to betray the Starks. Obviously his story has ended up changing massively since then, but who knows... maybe that's one element he decided to keep.
Now that Bran knows about Jon's true parentage, we can't see why he wouldn't spill the beans when he eventually makes it back to Winterfell. Then again it did take Bran a full four seasons to make it beyond the Wall in the first place, so who knows how long it'll be before he finally gets back to his hometown.
Whether the revelation comes in Season 7 or the beginning of Season 8, though, it seems inevitable that Jon is going to find out about his Targaryen heritage.