Spoilers for Game of Thrones Season 8 ahead. Sure enough, the Red Woman arrived to save the day and doll out some choice pieces of wisdom ahead of the Battle Of Winterfell. Sadly though, after helping out in the battle, Melisandre died on Game of Thrones. Well, maybe. The Red Woman just sort of collapsed, so who knows if she'll rise again, but it seems like her time in Westeros is most likely over.
She promised Davos earlier in the episode that she would be dead by dawn, and dead she seems to be. After arming the Dothraki with flaming weapons, giving Arya Stark a much-needed pep talk, and performing some other various magic around Winterfell, Melisandre's work was done. When the battle was over, and the sun rose, Melisandre walked out of Winterfell's gates, took off her clothes and her magic youth-bringing necklace and fell down into the snow. Considering that Melisandre has the ability to bring people back from the dead, it's hard to believe that she's gone forever, but let's assume for the moment that she is. She said she was going to die, and she's true to her word.
The only person who saw her do this was Davos, which is significant, as he's one of the only people who still wants her dead. She promised him that he wouldn't have to execute her, and she was right. It really seems like Melisandre's story is over now. If only she had done the folks at Winterfell one last favor, and burned all those dead bodies (you know, just as an added safety precaution) before she left. In the promo for next week's episode, it seems like they're doing it anyway.
Her time may be up, but what of her faith, and the other red priests and priestesses? Are they going to continue looking for their savior? With Beric Dondarrion also gone now, Game of Thrones lost two followers of R'hllor. More could still show up before the end of the season, especially if either Jon Snow or Daenerys Targaryen are destined to fulfill the Azor Ahai prophecy.
In Season 7, Melisandre left to go to Essos. Well, technically she was banished, and Davos and Jon Snow promised to execute her upon her return. Still, we don't know what she was doing in Essos, and the remaining episodes could reveal that. And why Jon should be thanking the Red Woman after all.
When we first met Melisandre on Game of Thrones, she was working with (and sleeping with) Stannis Baratheon. She usde king's blood to do spells for him and influence events in Westeros so that he could take the Iron Throne. After Stannis died, she supported Jon Snow, even going so far as to bring him back to life after he was killed on The Wall. In Season 7, Melisandre told Lord Varys that her time influencing Kings was over, but that she was destined to die in Westeros after making a quick trip to Essos.
Given all of her work before and during the Battle Of Winterfell, it seems like she lived up to that promise. Melisandre hasn't always been the most noble character on Game of Thrones, but at least she spent her final moments doing good for the realm and our heroes.