Before you can get COF inspection, you will need to fill out an MR14 form to change the use from a private passenger car (01) to a rental car (07), the form only takes a couple minutes to complete. There is usually a small licence fee associated with changing use. This fee depends on the model of your car but is typically around $20-$30. This is due to the change in ACC levies on a rental car licence as opposed to a private passenger car.
You can switch back to a private passenger car licence at any time by carrying out the reverse process at VTNZ.