We can absolutely insure your vehicle while you're using an overseas licence. There's no difference in the price of the policy, however a $400 'Inexperienced Driver Excess' would apply to the policy.
This means if you selected a base excess of $300 (for example) and had an accident, you'd need to pay an excess of $700 ($300 base + $400 inexperienced driver). You don't need to pay an excess unless you need to make a claim.
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The Inexperienced driver excess applies to anyone who has not held a New Zealand Full Drivers Licence for the last two years. If you're on an overseas licence, or NZ learners or restricted, this excess applies. It will continue to apply until you're had a NZ Full licence for 2 years or more.