Go to the category where your URL is and click "Update URL" in the upper right corner. You'll come to a screen where you can give all details about the old and new URL.
If you can include a clear and obvious note about the new URL somewhere obvious on the old site itself, that will also make it much easier for editors to verify that you really are the owner of both sites.
If the old site is already offline, then don't worry about it too much though.
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