According to the Code of the Republic of Kazakhstan "On the health of the people and the healthcare system", Article 162. "Examination for HIV infection":

Citizens of the Republic of Kazakhstan, Candace, foreigners, stateless persons, refugees and asylum seekers permanently and temporarily residing in the territory of the Republic of Kazakhstan have the right to voluntary anonymous and (or) confidential medical examination and counseling on HIV infection within the guaranteed volume of free medical care in public health organizations that carry out activities in the field of HIV infection prevention, in accordance with the procedure determined by the authorized body.

Thus, you can get a free HIV test in polyclinics at the place of attachment.