After successfully closing the Oblivion Gate outside Kvatch, your immediate priority is to assist Captain Savlian Matius in retaking the city. The city gates are still swarming with Daedra. Speak with Savlian Matius, who will formulate a plan to breach the city. You'll need to fight alongside the remaining Kvatch guards, pushing through the streets and eliminating Daedric resistance. This segment is combat-heavy, so ensure your gear is repaired and you have enough potions.
Your primary objective will be to clear the way to the Chapel of Akatosh, where Martin Septim is believed to be taking refuge. You'll encounter various types of Daedra, including Scamps, Clannfears, and potentially Dremora. Work with the guards, using their numbers to your advantage. Once you reach the Chapel, you'll find Martin and other survivors. After a brief conversation, Martin will agree to accompany you back to Weynon Priory. This concludes the immediate crisis in Kvatch and sets the stage for the next phase of the main quest.