If you renewed your passport and want to transfer the Australian visa to new one "in Australia" or "oversease"; you have a number of options that have been worked with some people:

First: If you have the electronic visa label:

1- Fill the 929 form and send to immigration office;

https://www.border.gov.au/Forms/Documents/929.pdf

2- Log into your immi account which you used during your immigration process to upload your documents. Go to "change address and passport details section" and update details [new passport number and new expiry date]. It can takes from 10 minutes to 2 days to be effective. To confirm that; you can log into the VEVO portal and check the updated details and print a copy as an extra confirmation.

3- Copy the old and new passport and email them to the nearest australian consulate if you are oversease.

4- Some people didn't know about the paper form or online way procedure. However, at the oversease airport the immigration officer contacted the Australian immigration department and they updated the passport details on spot with some delay. Of course this way is not recommended.

Second: If you oyur Australian vis is still the old paper visa label. In this case, you can use your new passport and attach to it the old passport with the visa label.