You cannot start a completely fresh "New Game" in Pokémon Conquest. It is a single-player strategy game with a fixed storyline and no "New Game" option after you've completed it or saved.
For a truly fresh experience with a new save file, you would need a separate cartridge (physical) or a different user profile/save slot if the platform supports it (3DS does not support multiple save files for this game). Consider trying a different Pokémon title like Pokémon Mystery Dungeon or the mainline RPGs.