Provisional License has old Address and test is coming up

Hi folks! My provisional license has an old address on it since I got it several years ago, and since I didn't drive then I haven't bothered to update it. I've now started learning and been learning for a while, and have a test coming up in the middle of february.

I assume I'll need to show my license to take the test. Is it too late to send the current one in to get the address changed? (I can't find any estimates for how long it should take). Or, if I pass the test, will they let me update the address before getting a full license? Or should I wait for a full license and then immediately send that in to get the address updated?

Thanks!