We applied for a partnership visa and the application was declined

A decline is not necessarily the end. Immigration New Zealand assesses partnership applications against criteria in its instructions, including that the relationship is genuine and stable, and that you live together in a marriage-like relationship, generally for at least twelve months. Check the decision letter for the specific reasons, since they show what evidence was found lacking. In some cases you can ask for reconsideration, providing new information that was not available at the time, and in certain circumstances you may have a right of appeal to the Immigration and Protection Tribunal, depending on your visa status and the type of decision. Deadlines are short, so contact a licensed immigration adviser or immigration lawyer. Gather strong evidence, such as joint tenancy or accounts, photographs, travel history and statements from family and friends who know you as a couple.