Great news! We're getting a new Harry Potter book!
The new book is actually a play, written by Jack Thorne. According to CNN, it's "based on an original new story by Rowling, Jack Thorne and John Tiffany". That could mean they literally wrote a short story together, or that they just came up with story ideas together. I'm leaning towards the latter.
The script is unfinished, in a sense. See, the play hasn't debuted yet. They plan to make changes to the script, while the play is still in preview mode. So a definitive version of the script isn't done yet. I'm sure they'll publish that separately.
The play comes in two parts, just like William Shakespeare's Henry IV. I doubt that's the inspiration, though. More likely, they're just following the lead of multi-part movies like The Hobbit, Hunger Games Mockingjay and Harry Potter 7. Sometimes, I think if they made the Harry Potter movie series today, there would be at least 12 movies...