In Greek mythology, Hesione was a Trojan princess, daughter of King Laomedon and sister of Priam. Exposed to a sea monster as atonement for her father's unpaid wage to Apollo and Poseidon, she was saved by Heracles; after his sack of Troy she was given to Telamon, bore him Teucer, and ransomed her brother Podarces with her veil — whence he was called Priam. She is the Trojan Hesione, not lesser namesakes.
Adapted from Wikipedia, "Hesione" · CC BY-SA 4.0
I.Family
Hesione is daughter of Laomedon of Troy and thus sister of Priam (Podarces), Tithonus, and other Laomedontids. After Heracles' first sack she becomes second wife of Telamon of Salamis and mother of Teucer (Teucros), half-brother of Ajax. Alternate notices give her a son Trambelus, or transfer that birth to another woman.
Dictys Cretensis once prints "Hesione" where the genealogy intends Pleione — a spurious conflation, not this Trojan princess.
II.The sea monster
When Laomedon refused the wage promised to Apollo and Poseidon for walling Troy, Apollo sent plague and Poseidon a sea monster (Cetus). Oracles demanded that Hesione be exposed; she was fastened naked to the rocks by the shore. Heracles, returning from the Amazons with Telamon and Oicles, agreed to kill the beast for the immortal horses Zeus had given in compensation for Ganymede.
He slew the monster — in some tellings after being swallowed and hacking free for three days — but Laomedon again refused the reward.
III.Sack, ransom, and later tradition
Heracles returned, killed Laomedon and most of his sons, and allotted Hesione to Telamon. Allowed to choose captives, she ransomed her youngest brother Podarces with her veil; from priasthai ("to buy") he was thereafter called Priam, and Heracles set him over Troy. Later storytellers make Priam's demand for Hesione's return a diplomatic prelude that Paris abandons for Helen — a secondary aetiology of the Trojan War.
This entry is the Laomedontid princess only.