Starting at the beginning of The Dark Knight a new player appears in Gotham.
Frank Castle from the newest season of Daredevil appears in Nolanverse Gotham with an arsenal of military grade weapons, no one knows anything about him.
What occurs now that Castle has set his sights on a worse wretched hive than the big apple.
For fairness sake, assume the events that lead to Punisher being Punisher still occured, simply in the Nolanverse New York (and without Daredevil or the MCU's involvement obviously).