Batman: Arkham Knight is not a game you can currently buy on PC. We still don't know when that issue will be resolved—although hopefully it's not before Rocksteady has a working PC version on their hands. Still, let's assume that it will eventually be available, and that we'll be able to buy its upcoming DLC.
The first bit of DLC is Batgirl: A Matter of Family. It's a prequel to Arkham Asylum, and will—as you may have gathered from the name—let you play as Batgirl. It's due out on July 14 for owners of Arkham Knight's Season Pass. At least, it is if you own the game on a platform where the game is actually available. On PC? Who the hell knows.
Here's the relevant plot details from WB's press release:
"When The Joker kidnaps Commissioner Gordon and holds him hostage at the Seagate Amusement Park, Batgirl and Robin must fight against the odds to save him and avoid falling victim to The Joker’s sinister plan. Trained by Batman, Batgirl’s combat combines with unparalleled hacking abilities to take down enemies, control objects and solve puzzles."