The Klingon Neutral Zone was more or less a mistake. Originally, the enemies in the Kobayashi Maru test were supposed to be the Romulans, which explained why they mentioned a Neutral Zone and all that. Then they changed it to Klingons without changing anything else so now there was a Klingon Neutral Zone too.
It's mentioned only once more, in TUC, but after that it's never mentioned again. Mainly because it was a mistake it existed in the first place.