If the module is 4G, you would not need a new module. As long as the current Alarm.com account is cancelled by your provider you can reuse the module with us.
Sensors will not be affected, they will populate in your new account when you connect your panel to your account.
Devices which connect to the backend directly like cameras, Liftmaster MyQ, lutron, Rachio, etc., will need to be added again to the new account.