There are so many possibilities, and I really can't say what's going to happen.
- Stannis defeats the Boltons, becomes king of Westeros: Though this is what so many fans want, it should be clear that Stannis will never rule. GRRM does not make much of an effort to conceal who the series' major heroes are, and as great and important as Stannis is, he's not a protagonist.
- Stannis defeats the Boltons, and ends up being betrayed by Melisandre: Personally, I think this is the most likely. A rift appears growing between Stannis and his "true queen", and her realization that Jon might be her messiah will certainly sour this relationship. I think it pretty plausible that Jon will be resurrected by Melisandre and arrive in Winterfell, now occupied by Stannis. My hope is that something in the crypts of Winterfell reveals Jon's pedigree. After shadow-killing Stannis and declaring Jon to be Azor Ahai reborn, Melisandre ensures that Jon Snow has the support of Northmen, any Targaryen loyalists, and worshipers of R'hllor.
- Stannis defeats the Boltons, but dies against the Tyrell-Lannisters: Unlikely. This would be a repeat of the Blackwater.
- Stannis defeats the Boltons, but is defeated by a Targaryen: Quite possible! I could potentially see Stannis briefly taking control of King's Landing before Daenerys or Aegon invades. This would call back to house Durrandon's last stand against Aegon I and his sisters. Should both of them defy all odds and live to the end of A Dream of Spring, Young Griff and Shireen could potentially end up being married.
- Stannis is killed by the Boltons: This is a possibility, but one I doubt. I'm not sure what narrative role another defeat would have. It essentially renders his post-Blackwater actions meaningless, and while D&D might not care about that, GRRM has different priorities.
There's also the "Stannis becomes the Night's King theory", somewhat hinted at by the text, but I find it a little too ridiculous. It's possible, I guess, but I don't know how that could happen at this point in time. Maybe in the show, but probably not in the books.