When will Apple TV + be launched in Kazakhstan?

Nobody here in the user forums has any inside information on Apple’s business decisions or policies, nor knows anything about what business changes they may be pursuing anywhere. Users here cannot answer your question as we simply don’t know why a service is available in some countries and not others. Only Apple could answer such a question, and they don’t participate here in the user forums.

The community would not know. Apple does not release information about progress in pushing out services to specific countries. They'll let you know once its out though. Of course, this is because of compliance to countries and other countries regulations.