You can change your civil union to a marriage (or your marriage to a civil union) without dissolving your current relationship. You need to complete a form and hold another marriage or civil union ceremony.
Celebrants can legally perform marriages and/or civil unions in New Zealand. If you want to become a celebrant, you can choose to be independent or connected with an approved church or organisation. Once you're registered you need to renew your registration each year and keep your contact details up-to-date.