Once inside the palace, head over to the right and through the open door. You are about to start learning about the new stealth system. When you get over to the door you will be prompted to start sneaking. Hit the prompted button and enter into the next room as there are guards looking out the window and ahead of you looking through the doorway.
Head over to the left and take cover behind the bed. Wait for the guards to move. When they do, head for the door. Sneak through the billiards room. Get over to the next open door. There is another guard in the next room. Duck into cover behind the couch. Wait for the guard to move over to the fire place. Slip over to the right and then make a break for the door. Head Northwest through the next room. Go over to the open door.
Head through the door and take cover behind the table. Head to the Right-hand edge of the table. Watch the guard until he leaves the room or moves. Head through the open window to the East of the table.
Turn to the left on the balcony. Use Free running to hop the gap and head through the next open door. This triggers a quick cutscene. After that it is back to the search for Elise.