Following is a New Zealand owned one. However, I don’t have any experience with them except some initial contact.

https://www.omf.co.nz/about-us

It is wise to do some home work on cost involved, customer service, integrity, reliability etc before selecting any broker.

http://www.investopedia.com/articles/00/112100.asp

10 Tips For Choosing An Online Broker

Please share your experience with brokers to identify some best brokers in NZ.