Public health services in New Zealand are free to New Zealand residents, so Clinical Psychologists working within the public health system will charge nothing to see you. Clinical Psychologists working in private practice will charge fees that vary considerably from one Clinical Psychologist to another. If you are not automatically told, you should always ask a private Clinical Psychologist what their fees are before you see them.
Some health insurance policies cover limited psychologist fees. Sometimes fees may be subsidised by government agencies such as work and Income, CYFS or ACC. If involved in these agencies talk with your case manager.