If you're a YouTube Partner, you can use the AdSense account that's connected to your YouTube channel to monetize your own site. You do not need to create another AdSense account to show ads on your site. Note that AdSense policies only allow one AdSense account per publisher.
Add your site to AdSense
To show ads on your site, you need to add the site to your sites list. AdSense will review your site and let you know when it's ready to show ads. You can then set up ads on your site.