It depends on the "Application" process, many covens on this site has Application that must be sent to the priest, priestess. and or both. This application can take as long as the Priest and Priestess wishes, this is because, they could for instance be letting their coven, council,..etc. vote on whether you enter.
Divine Essence for instance, allows our Council vote before we allow you to join. Now not every coven will tell you if you have been accepted or rejected, that is why, you should check frequently to see if you have. If you have been accepted, on your profile there will be a logo of our coven and our coven name on your profile.
It will also say; Coven Title: Member.