Someone has registered a domain name that matches my brand

Yes, the .nz Dispute Resolution Service, administered by the Domain Name Commission, handles disputes about .nz domain names. To succeed, you generally need to show that you have rights in a name or mark that is identical or similar to the domain name and that the domain name, in the hands of the registrant, is an unfair registration. Factors indicating an unfair registration include registering the name primarily to sell it to you or a competitor, disrupting your business or using it to confuse people. The process begins with informal mediation and can lead to an expert decision, at modest cost. Collect evidence of your brand use, such as trade mark registrations, sales records and their offer to sell. A trade mark registration significantly strengthens your position.