It seems like you have an urgent situation. You must apply for the next visa before the current visa expires. As long as you do that, you will get an interim visa, allowing you to stay in New Zealand lawfully.
1. The application forms you need are:
a. Partnership-based temporary visa application form (INZ 1198) https://www.immigration.govt.nz/documents/forms-and-guides/inz-1198-partnership-based-temporary-visa-application_april-2016_fa_web.pdf b. Form for Partners Supporting Partnership-based temporary entry application (INZ 1146) https://www.immigration.govt.nz/documents/forms-and-guides/inz-1146-form-for-partners_april-2016_fa_web.pdf 2. The application fee is $413. This can be paid by completing the credit card information on the application form
3. Current processing times for partnership-based work visas is about 25 working days (5 weeks)
4. You must include the following documents:
a. Application forms
b. Passport
c. Medical certificate (unless you have submitted medicals in the last 3 years)
d. Police certificates (unless you have submitted police certificates in the last 2 years)
e. Partnership evidence. You should include your marriage certificate, and also evidence that you are living together in a genuine and stable relationship. For example: phone bill, power bill, bank statements, insurance statements, photos, letters from family and friends.
If you are still unsure about your documentation requirements, I suggest contacting a professional adviser. You should also consider submitting a residence application at the same time because the documentation requirements are mostly the same.
This advice is given as general advice only and is based only on the information you have provided.