Recently renewed my KA/KSA membership, after it lapsed in Jan 2020. I had been in Brisbane, but now moved to Adelaide.

The new tag hasn't arrived yet, but I'd like to head out...... While I am waiting for the new tag, am I okay to display the old tag, then if challenged by relevant council, cite my member number?

Shouldn't be a problem mate. I generally keep a copy (on my phone) of the invoice or proof or renewal handy just in case whilst waiting for the tag to arrive.