The red dragon Meleys, also known as the Red Queen, is the dragon primarily associated with Targaryen princesses Alyssa and Rhaenys. Princess Alyssa is the mother of two major figures in the civil war: Viserys I, the king whose death sets off the succession crisis, and Daemon, husband of one of the claimants, Rhaenyra. According to "Fire and Blood," Alyssa took both of her sons on Meleys's back when they were just a few days old.
After Alyssa's death, Meleys is claimed by Rhaenys, daughter and heir of the late Prince Aemon, who was himself heir to the Iron Throne. Passed over in the line of succession largely due to being a daughter instead of a son, Rhaenys is known as the "Queen Who Never Was." Rhaenys sides with Rhaenyra, another passed-over female heir, during the Dance of the Dragons. During a great battle, both Meleys and Rhaenys are killed.
Based on her history in the book, it seems pretty safe to say that we'll see Meleys at some point during "House of the Dragon."