Keep any evidence that INZ returned to you from your partnership application, and continue collecting the same kind of evidence to show that you are still living together. You can apply for partner-sponsored residence whenever you have proof that you have been living together for at least 12 months - you don't have to wait till the end of your work visa. Even after you application has gone in, keep collecting evidence, because INZ commonly ask for more, just before granting the visa.
Here
https://www.immigration.govt.nz/new-...-resident-visa are the details about applying for the residence visa. Click on the red button near the bottom of the page to see all the details of what you need to do for the actual application.