Because Delphine and Esbern are always essential characters and cannot die it is not possible to kill them to protect Paarthurnax. ... However, you may still kill Paarthurnax at any time after this point; the quest will now reappear in your journal and can be completed normally.

Can you skip Delphine in Skyrim?

You can use a platter (find in dragonsreach) to glitch into the embassy, grab the dossier in the dungeon and that skips to the esbern quest. Goes right over some of Delphine.

Where is Delphine after killing Paarthurnax?

Look for Delphine in the room with the Alduin's Wall (screen above) or by the outer observation point.