Upon completing all of the other quests for Kyra, you are going to unlock this one. Head to the stage on the map to trigger a cutscene with Barnabas.
He will summarise your progress on the island. You’ll be requested to say your farewells to the people of Delos.
Both are around the southern shore, so head there. Head to the eastern you to Speak to Kyra.
Provided you did not rat her out to the rest of the island, you’re help her in sending Podarkes to the ferryman.
Thaleus will be about the beach and not in the best of moods, particularly if you seduced Kyra, so you may need to kill him.
You have the option to speak to Kyra before wrap up the celebration, but it is likely not the best option. When you plan to disembark, Sokrates will greet you.