Have just re-joined free Avast. In no time a message arrives in my former mailbox closed ca 18 months ago.
Admittedly this sort of thing arises from other sites and has proved hard to get rid of.
Go to the Avast UI > Menu > My Subscriptions > Go To Account.
Once open go to the Email management > Add another email address - your new one.
I’m now working from memory (or guestimate) you should get an email confirmation on that new email (and possibly the old one that it has been changed) ?
Now go back into the Email management > and set the new email as your Primary (default email address). Leave the old one until you are sure the new one is the one shown in the Avast UI > Menu > My Subscriptions. If so you could remove the old one, but I would suggest there is no rush, that last thing you would want is to be locked out.