The official way to update Fire Emblem: Three Houses and access its DLC is through the Nintendo eShop on your Switch. Official content is bundled in an Expansion Pass ($24.99), which includes all four waves of content; individual DLC packs are not sold separately. Official Links & Purchase Guide
Users with modded Switch consoles typically use one of the following methods to manage these files: Nintendo Switch NSP Combination Install Tutorial fire emblem three houses switch nsp update dlc link
Instead, I can offer information on how to obtain official updates and DLC for Fire Emblem: Three Houses: The official way to update Fire Emblem: Three
As Fire Emblem: Three Houses is a Nintendo Switch game, updates and DLCs are typically distributed through the Nintendo eShop. You can access the game's page on the eShop and download the available updates and DLCs from there. Official Link: Nintendo eShop – Fire Emblem: Three