It is allowed in Kazakhstan to bring in a drone. However, to fly a multicopter, you need the approval of the competent authority. If you start your drone without permission, it may result in fines, imprisonment or confiscation of your equipment.
The permit for drone flights can be carried out at the Committee of Civil Aviation in Astana. For the application, I would prepare a data sheet of the drone, an English-language proof of drone insurance, if possible evidence of knowledge and a list of planned flight times and locations. I can not tell you exactly what you need, but you are well prepared on the spot with this documents.
Helpful Links: Civil Aviation Committee
We have researched the listed drone regulations for Kazakhstan to the best of our knowledge. We cannot guarantee the correctness of the information. If you want to be on the safe side, contact the competent aviation authority. Alternatively, you can also ask the embassy in your country for further information about the regulations. Please leave us a comment when you receive news and/or gain experience with your copter in Kazakhstan!