If I am in an Inactive/Dropped status should I create a NEW membership application?

No.  Please do not create a new membership application.  Duplicate membership record situations are problematic and could cause delays in both processing and event registrations such as tournaments. If you have a Player Rating, it will not be dynamically posted to the new record.  It is always best to renew, to keep your information consistent and current, and to avoid special handling and delays.