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In an interview with Game Informer, the director of the Kingdom Hearts series, Tetsuya Nomura, confirmed that there are still more Disney worlds left to be revealed. Game Informer states:
As to the decision to revisit Jack Sparrow and the rest of the POTC gang:
And on the subject of DLC:
Source: Game Informer Link 1 & Game Informer Link 2

As the tweet above indicates, 'Kingdom Hearts III' will be one of the games focused on in the 'PlayStation Live From E3' program, with the focus on the game scheduled for 2:15 p.m. PDT on Tuesday, June 12th, which you'll be able to watch from live.playstation.com.

EDIT:

Here's the KH3 portion of 'PlayStation Live From E3':

'Kingdom Hearts III' is now available to pre-order from the PSN store (as seen above). Pre-order bonuses include a theme as well as a Star Seeker variant Keyblade.

After releasing the shocking trailer during Sony's E3 conference confirming the return of Jack Sparrow and the rest of the POTC gang, Square-Enix also revealed that the 'Pirates of the Caribbean' world, called 'Port Royal' in KH2, will instead be called 'The Caribbean' in 'Kingdom Hearts III'. In addition to that, the world logo as well as renders for Sora, Donald, and Goofy from that world have been released. Check 'em out below:
Updated with higher quality renders:

EDIT:

Even MORE renders:

Update (and edited): The limited edition that includes the PS4 Pro will include Kingdom Hearts III, and DLC for a special keyblade, and a special theme (likely the same included with the digital download preorder of Kingdom Hearts III). This version can be found on the Japanese Playstation page (but doesn't include preorder information). The price for this is ¥ 53,780 + tax. This is ONLY for Japan, currently.

Original:
We weren't kidding when we said Sony dropped a lot of Kingdom Hearts news! After all these Kingdom Hearts games... we're finally getting a Kingdom Hearts 3 PS4 (Pro) in the West (we're assuming since they announced at at E3).

Unfortunately, nothing else is known about it, so we'll have to let you know when we know more!

EDIT:

Here's what the special theme mentioned above will look like: