kuvesa tokhesa - "I serve willingly." A willing servitor. The Federation may translate Kuve as slave but the Klingons seem to have a more nuanced version. The conquered planets serve the Empire. If they rebell then action would be taken against them. Kor seemed willing to let the Organians continue to live much as they had as long as they behaved themselves. He on;y ordered the group of hostages killed after Kirk & Spock decided that the Organians shouldn't be able to decide for themselves how to deal with the Klingon occupation. It's not like Kor beamed down and started slaughtering people just to make a point.
KOR: Good honest hatred. Very refreshing. However, it makes no difference whether you welcome me or not. I am here and will stay. You are now subjects of the Klingon Empire. You'll find there are many rules and regulations. They will be posted. Violation of the smallest of them will be punished by death.
AYELBORNE: We shall obey your regulations, Commander.
KOR: From this day on, no public assemblages of more than three people. All publications to be cleared through this office. Neighbourhood controls will be established, hostages selected. A somewhat lengthy list of crimes against the state.
Basically, don't make waves. Harsh by human standards but nor mad dog crazy either. How do you think the Afghans and Iraqis were treated just after the war started? I'm sure there were various regulations put in place as well.