Here is a list of all post-game contents that can be unlocked after beating the main story of the game.
Chapter 6 Unlocked
If you save your data after the ending of the main story, you will be able to unlock a new additional chapter in the game.
In this chapter, you move around the map freely with both the Alm and Celica army joining forces. The leader in the chapter can be switched between Alm and Celica.
In addition, the battle dungeon “Underground Labyrinth of Thebes” will be unlocked.
Sound Test and Movie Viewing
The Sound Test and Movies menu will now be unlocked under “Extras” found on the main menu screen.
No Lunatic Mode
Even after you beat the main story chapters, the game does not have a Lunatic Mode that is found in most Fire Emblem games after clearing the main story.