Uncharted 4: A Thief's End marked the end of Nathan Drake's story earlier this year, but Naughty Dog confirmed prior to launch we will be getting some single player DLC later down the line. Naughty Dog hasn't given any details to whether or not the DLC will focus around Drake or his brother, Sam, but we may have some new information regarding details on when exactly we can find out more about it as well as who it's about.
LetsPlayVideoGames recently got the chance to interview Troy Baker who plays Sam in Uncharted 4 and got him to dish some details on the DLC. Baker labeled the DLC as "by far the biggest story DLC [Naughty Dog] have done” and said he believes the reveal will be “very soon”.
LPVG also corroborated with sources and confirmed the DLC will be playable without owning a copy of the main game, similar to The Last of Us' Left Behind DLC. We also got some other details, but they involve spoilers from the main story of Uncharted 4, if you haven't beaten the game, you may want to click off this page.
LPVG also mentioned that Nolan North (who plays Nathan Drake) and Baker had some ideas for the DLC that were to involve Cassie Drake, Nathan Drake's daughter who we meet at the end of Uncharted 4. Naughty Dog's writers however may have had better ideas that don't involve Cassie. “[I] imagined [them] going on an adventure with Drake’s daughter, what the writers came up with was far better than the ideas [they] could come up with”
One can probably assume that the DLC will take place prior to the events of Uncharted 4 and may follow Sam and Nate's adventures before the two brothers got separated after the prison break that ended with Sam getting critically injured and left behind. Nathan Drake seems to be out of the game after Uncharted 4 as he has a family and has resided to taking jobs that don't involve him getting shot at or putting himself in danger, so it's unlikely this will be set after Uncharted 4.
LPVG also believes that the DLC will be revealed at Sony's PlayStation Experience event which will take place on December 3rd and 4th.
Keep in mind these are rumors, so take it with a grain of salt but it seems likely it could be revealed at PSX. Sony likes to reveal things at the fan event each year and showed off the first Uncharted 4 gameplay at PSX two years ago so you can probably assume we will get some sort of details about the DLC in December.