Assuming that you intend to depart and return before your current visa expires (and any Interim Visa) kicks in, it's dependent on your visa conditions once again. Your eVisa letter (or visa label) will tell you whether your visa is valid for single or multiple entry, and also the last date that you may travel and re-enter to New Zealand if your visa is valid for multiple entry.
If you have a single entry visa, or a multiple entry visa where the last date that you may travel and re-enter to New Zealand is before your intended date of return (but your intended date of return is before the visa expiry date!), you may
apply to vary your visa's conditions.
You can not travel after your visa expiry date, until you are granted a new visa. Note that doing so will not necessarily halt processing on your new visa application, but it will prevent you from returning to New Zealand until your new visa is granted. Interim Visas are only granted if the applicant is onshore, and do not have travel conditions (
I1.20).
Finally, I want to clear up a misconception you may have around Interim Visas. They exist solely to maintain an applicant's lawful status in New Zealand while their further temporary visa application is being considered (
I1.1). As such, they are not granted automatically simply based on having an application for a further temporary class visa in INZ's systems; INZ will only grant one if they believe that your current visa will expire before a decision is made on your further temporary class visa (
I1.5 and
I1.10). An Interim Visa, if granted, only becomes valid when your previous temporary class visa expires, and never becomes valid if a decision is reached on your new temporary class visa (
I1.15). (This last scenario happened with me. I was on a Visitor Visa and had a Work Visa application in the system. INZ issued an Interim Visa around a week before the Visitor Visa was due to expire. The next day, the Work Visa was granted, and so the Interim Visa was cancelled without ever having come into effect.)