If she intends to apply for a partner-sponsored temporary work visa, you should be aware that INZ only recognizes partnership as being a provable live-in relationship. You have to provide evidence of living together, and we know from experience that they take applications with around three months of evidence
https://www.google.co.uk/#q=site:enz...tnership+proof seriously. Those old threads have a lot of discussion and suggestions which should help somewhat.
If you have enough evidence to lodge her application any time before her WHV runs out, she will be automatically covered by an Interim visa while the case is being processed. Keep collecting evidence during the processing - INZ routinely ask for more just before the visa is issued. And in any case, you will need all this early time still covered for when you apply for her next visa. Keep copies and notes of what you send in, and remember, overkill is good for this purpose.
As the INZ partnership requirements are not based on marriage, your previous/existing marriage should not be a problem. But it will probably make life easier for the official who works the case if you can show clear evidence of NOT being with your wife (i.e. at a different address), before you set up home with your new partner. Obviously, if you had a legal separation or similar, that would also help with the application. Here are the actual requirements for the NZ partner.
http://www.immigration.govt.nz/migra.../nzpartner.htm