Rhaegal the dragon definitely dies in Game of Thrones Episode 4.
With Melisandre dead and the Night King shattered into a gajillion icy shards, Game of Thrones has returned once and for all to the rational, magic-free world of the living, minus, you know, the dragons and Zombie Mountain and other affronts to realism. In this cruel world bound by the rigid laws of dragon anatomy, Euron, Cersei, and the Golden Company know that if it bleeds, they can kill it.
And boy, does Rhaegal bleed. He's still injured from the Battle of Winterfell, sure, but seems to be flying around just fine with Drogon and Dany at his side as the Northerners approach King's Landing. (Jon Snow isn't riding Rhaegal because "he needs to heal," even though Tormund points out that he weighs as much as "two fleas fucking." Hey, if Jon were riding him, then he'd be dead, too, which isn't going to happen.) Suddenly, a giant arrow hits him in the chest. Then another straight through the neck. The next thing you know, Tyrion and Varys are watching Rhaegal splash into the sea, 100% dead, leaving Dany and Drogon as the only significant battlefield advantage the North has. Still, one fire-breathing dragon and his very angry mother is infinitely better than a bunch of wildfire and a swashbuckling, overconfident Greyjoy.