Exporting fresh potatoes is possible from New Zealand but there are strict phytosanitary rules governing the entry of potatoes in foreign counties. The first step is to establish what the ICPR (Importing Countries Phytosanitary Requirements) are for the destination country. ICPRs are documents published by the New Zealand Ministry of Primary Industries to help exporters find and meet other countries’ importing requirements for plants and plant products, see here for more information
You will need to check the country’s requirements for importation and what the import health requirements are. It is best to contact a Potato Exporter to help facilitate the process. Here is a list of exporters.