Ever since their Season 3 road trip around Westeros, Jaime Lannister and Brienne of Tarth have been the dark horse of Game of Thrones ships. They had snarky chemistry and an unspoken understanding of each other; they were two characters who worked together unexpectedly and that made them fun to watch. No one in Westeros seems to appreciate just how awesome Brienne is and she'd been suffering in unrequited love for so long that it's understandable fans want to see her finding some romantic satisfaction. However, moving on with a guy who has spent his entire life devoted to his sister might not be the best love connection to make (just sayin'). Still, could Jaime and Brienne get together on Game of Thrones?
After a long time apart, Jaime and Brienne will be reuniting in Season 6, Episode 8, "No One." Brienne is on her way to Riverrun under orders from Sansa to see if the Tully army might be willing to join in the fight against Ramsay. Jaime is there trying to help the Freys in their siege of Riverrun, which they are attempting to get back after capturing it post-Red Wedding and subsequently losing it again to Brynden Tully. Could romance blossom under such deeply questionable circumstances?
Well, it is Game of Thrones, so there could be worse meet cutes.
The biggest roadblock between Brienne and Jaime is that he's still totally in love with his sister and he's never really looked elsewhere. His only relationship has been a toxic, unhealthy one that neither sibling has ever been able to find their way out of. It's made even more difficult by the fact that Jaime's sister is Cersei, who isn't exactly known for being open and forgiving. Personally, I can't imagine that she'd ever be okay with letting Jaime get away. Plus, now that Tormund is in the running for Brienne's heart, it looks like Game of Thrones might have a serious shipping war on its hands.
Realistically, it doesn't seem like romance is in the cards between Jaime and Brienne. Logistics have mostly kept them away from one another and will likely continue to do so if Jaime returns to King's Landing and Brienne to the North. Their relationship is strictly platonic in the books so far, too, so there's no helping hand to be gained there (though there are still a couple of books to go!).
Actress Gwendoline Christie is a fan of the pairing though she's fully aware of the forces keeping them apart. She told Rolling Stone that Jaime and Brienne have "a bond that is quite unusual and quite pure," and that she understands why fans still yearn for them to get together. Still, nothing is ever simple on a show like this one. "[...] we all want to see the impossible actually happen, to see these two extraordinary characters reach that amazing stage," Christie said. "Everyone's a sucker for some love and romance and whatever that may bring. But with those two? Lord knows."
But just because their romantic future is far from assured doesn't mean fans can't enjoy every bit of interaction they have anyway – that's half the fun of shipping.