That's really for temporary entry class visas (
E3.10(a) and
E3.11) and not so much for resident visas as a resident visa is valid indefinitely (
RA1.1) -- but note that you must have a valid passport at the time that your application is (hopefully favourably!) decided, as an expired passport is an "unacceptable travel document" due to not meeting the definition of "passport" in
A2.1.1 and visas therefore cannot be endorsed in them.
In your place, I would continue to submit the Resident Visa application in December, but also simultaneously lodge an application for passport renewal with HMPO, and submit a cover letter advising INZ of this fact. Then, if my new passport arrives before the Resident Visa application is decided, I would notify INZ of this and prepared to submit the new passport to INZ for physical verification; if my new passport arrives after the Resident Visa is favourably decided and endorsed in the old passport, I would follow the
standard visa transfer process.
You will have to submit your old passport to HMPO to be cancelled (this was the case in 2019 when my partner renewed her UK passport, and I have no reason to believe that this has changed). INZ will, per
RV2.40, accept a certified copy of your passport, so get this done before you renew it -- once you courier it off to HMPO, you will not see it again until your new passport is issued, at which point HMPO will return your old passport with your new passport (in separate courier bags, so don't be alarmed if one arrives and not the other).