Set in the same post-apocalyptic world as the game, it's called What Remains, and regardless of how the acting or story turns out, boy, they're using some expensive gear. This looks better than a lot of TV shows.
What Remains is being made by Manifest Film, and what you see above is a clip from a pilot episode. While the project's site makes no mention of support or backing from Sony or Naughty Dog, we're checking in, because this looks awfully expensive (and premature) for it to be simply fan work.
What Remains [Official Site]