I have killed Alduin, but no one will give me quest to kill partharnax

None of my active quests are from the blades or graybeards. I have talked to partharnax, Delphine, esbern, and arngeir, and none will trigger the quest to give me the option to kill or spare partharnax. I can’t even get a quest from angeir to look for more words of power. What am I missing here?