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I think DPS is supposed to mail you a notice, but you can take the class any time within 6 months of expiration, even if you haven't received the notification.

As for renewals being separate from new, I've done classes with both. We usually cover all the stuff that is common to both groups, then go to the range. After that, we send the new guys to lunch while we finish up and test the renewals. I've also done classes that were just renewals. It's pretty much up to the instructor you choose.