https://wccftech.com/druckmann-no-plans-last-of-us-part-ii-dlc-silent-multiplayer/

There are no plans for The Last of Us Part II DLC according to Naughty Dog's creative director and Vice President, Neil Druckmann.

The original The Last of Us received additional story DLC following the game’s PS3 release in 2013, and the Left Behind expansion was included with the remastered PS4 version of the game.  From the looks of it, however, The Last of Us Part II won’t be receiving any additional DLC. At least, there are currently no plans for it.