Zeus is correct. Only Petrarca can appoint someone as Coven leader or move a Coven from the inactive to the active list.
In order to take over an inactive Coven you must send an e-mail to Petrarca explaining why you wish to take over a group and what your qualifications are for leading that particular Coven. Pet will then look over a number of different factors including how long you have been a member of SOM, the contributions you have made, your ability to guide others, your maturity, etc. He will also be looking at whether or not there is any need at the moment to reactivate an inactive Coven. Once he has considered all the pertinent factors he will make a decision.
Since Pet is a very busy man the answer to your application may not be quick in coming. But if you have applied and several weeks go by then it is likely that you have not been approved for Coven leadership.