Fans have been waiting literal years to see Jon and Daenerys meet and now that it's finally happened, will Daenerys and Jon Snow work together on Game of Thrones? They both have something to gain from the alliance, but how deep it ends up going remains to be seen. As of the third episode of Season 7, Daenerys has agreed to allow Jon to mine some dragonglass so he can make weapons to defeat the White Walkers, but if they can work together to use each other's armies, they can gain a lot more than just the dragonglass itself.
Although Daenerys has three different armies at her disposal already, she did just lose most of the Iron Fleet, so allying herself with Jon's men in the North as she tries to take over Westeros could benefit her greatly. On Jon's end, if he could gain an ally in fighting the White Walkers — which, let's not forget, many still don't believe are real — it would mean a lot for the great war to come.
As Jon said himself, the fight over the Iron Throne means pretty much nothing if the ruler left standing has no one left to rule over. So Jon and Daenerys working together on Game of Thrones could benefit both parties involved.
During Jon and Daenerys' first meeting, we saw Daenerys focused on getting the Iron Throne and Jon arguing that her goal is pretty much irrelevant in light of the White Walkers, proving that they both have very different goals. We know Jon is right: we've seen that the White Walkers are indeed a much bigger thing to worry about than Cersei's reign of terror. If Daenerys can come to understand that too, then she and Jon could indeed have what Tyrion calls "a productive working relationship" while she pursues the throne.
To be fair, Daenerys has a rightful claim to the Iron Throne, but Jon's problem in the North is simply more immediate than hers. In the preview for Episode 4, Daenerys says that she lost some of her bigger allies, so now more than ever she's going to need Jon's help. But if she comes to need him more than he needs her in terms of numbers, getting Daenerys to work with Jon might come a little more easily.
She already budged at the whole making him bend at the knee thing, so she's obviously got some ounce of respect for him. And as we all know (but they don't yet), they're actually family, so in the end, Jon and Daenerys' plans should sync up pretty well.