Your application is still inside the Pet's files. What they mean by proving yourself, is that you must show Pet your worthy of leading a coven. This is by posting knowledgeable stuff onto the forums, chat, articles, and spells.
Just remember that applying for a coven will not make it 100% guarenteed that you will get it. You got to work hard (but don't spam) on getting it. Proving yourself to Pet you want it and can actually lead it. Now inactivity will probably not be a good thing, because Priest and Priestesses can not be inactive for a long period of time, otherwise their coven ends up in the inactive section.