The Organians never impose a NZ between the Federation and the Empire.
There is a treaty in the Franz Joseph TECHNICAL MANUAL describing the zone ("750 parsecs in width"). Although that is not "canon," it is a logical extension of the episode, since the Federation and the Klingons knock heads in later episodes (e.g. "Day of the Dove", "Elaan of Troyius"). Obviously the Organians did not continue to immobilize Federation and Klingon vessels everywhere
, even though that was Ayelborne's original statement.
The "Organian Peace Treaty" is mentioned specifically in "The Trouble with Tribbles." Although, it is interesting that the bar fight could even take place (illustrating just how much hot water Scotty was in). I guess the Organians have nothing against drunken brawls, but draw the line at ulama
and anything more intense.