It seems as though The Legend of Zelda: Tears of the Kingdom has already begun to tease upcoming DLC. On the Zelda official website, double-asterisk note at the bottom of the Tears of the Kingdom page remarks “full version of game required to use DLC. Sold separately.” What is notable about this is that there is no other double asterisk note on the page, meaning that this may have been a mistake on the part of the Zelda team releasing this information earlier than planned. According to Gamespot, Nintendo has not officially announced any support for the game after its initial release, however, this provides a pretty strong indication that we will be getting some in the future.
Even before this leak of information, fans had been expecting that Tears of the Kingdom would have some form of DLC, solely going off of the previous iteration of the game. The Legend of Zelda: Breath of the Wild has two separate DLC packs and new treasure items that give cosmetic items such as a shirt with the Nintendo logo crest on it.
The reason this is important in providing context for upcoming DLC in Tears of the Kingdom is that the same message regarding the full version of the game requiring DLC is at the bottom of the Breath of the Wild page as well. While this does not confirm how many DLC will be available in Tears of the Kingdom, there is a correlation between the two and their references to having DLC at all.
With The Legend of Zelda: Tears of the Kingdom releasing on May 12, 2023, fans will likely have to wait months for DLC to come for the game, but with the upcoming RPG having the largest file size of any first-party Nintendo Switch game according to IGN, there will likely be plenty of content to satisfy players until the DLC eventually comes.