It was a year between the Kronos incident and the end of the movie. If the Klingons hadn't started a war in that time, the incident was likely taken care of through backdoor diplomatic channels.
I hadn't even thought about that, but you're right. Good catch.
I wonder if Starfleet had to give something up to the Klingons to maintain the Cold War status quo after Kirk and Khan destroyed one of their ships and killed a patrol. You could almost imagine something like the Augment/Klingon virus arc on Enterprise
where Section 31 or Starfleet itself quietly makes a back door deal to give the Klingons Augment DNA to prevent a war. The Klingons don't like how easily their warriors were defeated so they want the Augment DNA to create supersoldiers.