At this point you get to choose who you take along in your party, so Edgar doesn't play a specific role anymore. I'll just briefly summarize what happens
The party headed off to the direction Terra flew away to, and they eventually found her in Zozo. ( on the way they will pass Figaro castle, and if you have both Edgar & Sabin in the party, this is where the coin toss flashback occurs ). Ramuh was with Terra, and he asked the party to go to the Magitek factory to rescue his Esper friends, as one of them would able to help Terra recover her memory. So, Edgar suggested that they should split up to two groups again, one will stay at Narshe while the other head to Magitek Factory. The party going to Magitek Factory needed a form of transportation, so they headed down to the Jidoor/Opera house area for help. They heard words about Setzer and his airship, the Blackjack, so they had Celes pose as the singer Maria, whom Setzer was planning to kidnap. They got into Setzer's airship when he abducted Celes, and after some convincing they got him to help them. ( If you have Edgar & Sabin at this scene, Edgar's double-headed coin would be revealed here ). They arrived to the factory, retrieved the magicites of the Espers, and headed back to Zozo. Terra recovered her memory with the Maduin Esper, and they headed off to the Sealed Gate to the Esper world to have Terra convince the Espers to help them. The Espers went berserk when the gate opened, and as the party tried to escape Edgar lost control of the airship and crash landed in the Empire's territory. ( and he was supposed to be the master of machinery...this is certainly not one of his finer moments ^^ )
At the same time, the Returners launched an attack on Vector, only to find the city already in flames. The Emperor expected the party's arrival and invited them for dinner, stating that he had a change of heart. At dinner, the Emperor stated that he had been wrong the whole time, and that he wanted to end this war. He asked Terra to talk to the Espers to help them understand that the war was over. Knowing that the Emperor couldn't be trusted, Locke and Terra went to find the Espers with General Leo while Edgar and the rest of the party stayed at Vector to find out the Emperor's true plans.