According to a livestream that aired today on the official Naughty Dog Twitch Channel, Uncharted 4: A Thief's End's single player DLC won't be seen or heard from for quite some time. Their exact words were "it will be a while" when referencing when we could hear something about it.
To be fair, Naughty Dog did say that production on the currently unnamed single player DLC didn't begin until after the full game released back in May, so it's not hard to see why there aren't any concrete details.
Back in November, Naughty Dog admitted that they had no idea what they were planning on doing for the DLC, since they wanted to put all of their focus into the main game (which was a massive success). The studio acknowledged that single player DLC "worked really well for us for The Last of Us," so the feeling was that they could "put together a really great piece of content as well [for Uncharted 4]."
