Use an agent for Zambia, don’t even bother to contact the CAA directly. You’ll need to get a TEMPORARY AIR SERVICE PERMIT (TASP) for any cargo or passenger operation, the agent will facilitate this for you. American Flight Support will be able to help, please get in touch with your requirements.
Official documentation states they want the application at least 24 hours prior to operation, but our experience is to give it between 48-72 hours.