There is no price to pay or a debt to be filled. Melisandre and Beric say on multiple occasions that the people that have been brought back have done so because they have a purpose to fulfil.
Melisandre: I interpret his signs as well as I can. If the Lord didn’t want me to bring you back, how did I bring you back? I have no power. Only what he gives me and he gave me you.
Melisandre: I don’t know. Maybe you’re only needed for this small part of his plan and nothing else. Maybe he brought you here to die again.
Jon: What kind of god would do something like that?
Melisandre: The one we’ve got.
Game of Thrones, Season 6 Episode 9, "The Battle of the Bastards"
Melisandre: The Lord brought him back for a purpose. Now that purpose has been served.
Game of Thrones, Season 8 Episode 3, "The Long Night"
However, it's not clear what that purpose is, as said above, Melisandre even states later on that she thinks it might be because of his part to play in the battle against the Army of the Dead.
Daenerys: What does your Lord expect from me?
Melisandre begins speaking Valyrian again.
Melisandre: The Long Night is coming. Only the prince who was promised can bring the dawn.
Daenerys speaking in English.
Daenerys: The prince who was promised will bring the dawn. I'm afraid I'm not a prince.
Missandei: Your Grace, forgive me, but your translation is not quite accurate. That noun has no gender in High Valyrian, so the proper translation for that prophecy would be the prince or princess who was promised will bring the dawn.
Tyrion: Doesn't really roll off the tongue, does it?
Daenerys: No, but I like it better.
Daenerysturns back to Melisandre.
Daenerys: And you believe this prophecy refers to me?
Melisandre: Prophecies are dangerous things. I believe you have a roll to play, as does another. The King in the North, Jon Snow.
Game of Thrones, Season 7 Episode 2, "Stormborn"
It's safe to say that as he hasn't died that his purpose is unfulfilled. Maybe he'll become the King beyond the Wall and lead the free folk, they certainly seem to trust him. Or maybe he'll die on the trip to a suitable place. We don't know what his end purpose is because we don't see it.