What should I do after renewing my passport while holding an OA retirement visa in Thailand?

You're a YEAR away from needing to do anything about it.

However, once you do get a new passport, at least in Bangkok to get the stamps transferred you will need to show another bank letter and updated bank book (if you used banked money for this current extension) <- to make sure you are still meeting the financial requirements for the whole year.

AND

again in Bangkok you will need to have the following copies and the transfer stamp form filled out.

Or carry both until you get a new stamp.

I assume you mean doing from Thailand so pretty sure you can renew your passport early so I’d think do that via the (Oz?) embassy before you go for your next extension. Just leave enough time! You maybe won’t need to transfer to you old passport but take both to Immigration

When you get your new passport it should come with a letter from your home country Embassy to Thai Immigration requesting they accept your new passport.

Your new and current OA extension stamp (its no longer a visa) just obtained will be transferred into your new passport to use.