Theoclymenus tells Penelope that Odysseus is back on the island. He states that the king is busy gaining information about suitors’ evil deeds. The king is preparing his revenge. Penelope doubts his words but promises to reward him if the prophecy comes true.
Detailed answer:
To start with, Telemachus first meets Theoclymenus in book 15. The latter joins Telemachus on his trip to Ithaca. He has to flee from Argos after killing a man. Homer introduces Theoclymenus as a seer. He is the son of Apollo’s greatest prophet, Polypheides. Upon arrival to Ithaca, they see a hawk flying by with a dove in its claws. Theoclymenus knows it is the messenger of Apollo. He tells Telemachus that it is a good sign. He predicts that his house will rule Ithaca forever. Just as Penelope later, Telemachus promises to reward the seer shall his prophecy come true.
When Telemachus and Theoclymenus meet Penelope, she asks them to tell what they know of Odysseus’ fate. By that time, Telemachus has already met Odysseus. He wants to put his mother at ease. Yet, the father forbids him to tell anyone about his return. Telemachus does not dare to reveal that his father is back on the island. Instead, he says that Odysseus is held captive but alive. This information makes the seer disagree. He says that the king is indeed lives and back on the island.
The seer does not reveal, though, that Odysseus plans a strike. Yet, the information told is enough to prove that he is a real seer. Unlike Telemachus, he has not met Odysseus yet, but his information is accurate. However, Penelope does not seem eager to believe any of it. She wants to but does not allow herself. But the prophecy confirms. Odysseus reveals himself later and fights the suitors.