Syrax
Rhaenyra's dragon since girlhood, well fed, well housed, and never much blooded.
The beast itself
Syrax was yellow, and glossy with it. She was fed by hand from the day she hatched and it showed: heavy through the shoulders, thick in the tail, her scales kept polished by keepers whose whole office was to keep her looking like what she was, which was a queen's ornament as much as a queen's mount. She was large ÔÇö larger than most of the young dragons of the Dance ÔÇö but the size was the size of an animal that had never had to catch anything.
Her temperament was the temperament of a pampered beast: not gentle, exactly, but incurious and slow to trouble herself, accustomed to people, and inclined to complain rather than act. She would come to a call, which very few dragons will. She would let strangers stand nearer than any dragonkeeper thought wise. What she would not do was hunt, or fight, or manage the sort of tight, mean flying that beasts raised half-wild on the Dragonmont did without thinking. Left chained in the Dragonpit for long stretches, she grew loud, restless and fat, and she was named for a goddess of the old Freehold, which nobody thought ironic at the time.
Her rider: Rhaenyra Targaryen
Rhaenyra had her from girlhood, and for a long while the pairing was the pleasantest thing in either of their lives. A princess barely into her teens flying her own dragon over Blackwater Bay while the court below argued about her inheritance is one of the more attractive images the dynasty produced, and the two of them were genuinely well matched at that stage: young, conspicuous, unbothered.
What they did together, over thirty years, was almost entirely ceremonial. Syrax carried Rhaenyra to Dragonstone and back, to feasts, to weddings, to her father's councils, and above all to be seen. When the war came, the queen flew her in earnest exactly once that anyone recorded, and even then the point was arrival rather than battle: Dragonstone taken, the crown claimed, the black council convened with a dragon breathing in the courtyard. After that Rhaenyra kept her close and used others' beasts to do the fighting, which was strategically sensible and did nothing for either of them.
From outside, the bond read as ownership rather than partnership ÔÇö the one royal dragon anybody could reliably point to and name, chained where the city could hear her, in a pit built by the family precisely so that the city could hear her.
What became of it ÔÇö if an ending is written, it is here. Spoilers.
Syrax died during the storming of the Dragonpit, when the starving mob of King's Landing came for the dragons with spears and hooks. She killed a great many of them and they killed her anyway ÔÇö the first time in history that common people brought down a dragon with their hands.