There's no need to open another account or notify us when you place ad code on a new site. Once your account is approved, whenever you place your AdSense code on a new page, we'll automatically associate that new site with your account.
Just generate the AdSense code as you did for your original site, and add it to whichever page you'd like -- making sure, of course, that it complies with our program policies. You don't need our team to officially review your site beforehand, but please use your best judgment to make sure that your site content and ad implementation are compliant. (Our policy explanations might help.) We regularly review sites displaying our ads, and we'll let you know if we find any issues.
Note that if you're using the Allowed Sites feature, you'll need to add the new URL to your Allowed Sites list, or you won't receive any earnings for that URL.
We look forward to helping you monetize your new site!