The EASA C of A is a document that is issued for the life of the aircraft
The ARC is issued for one year and then renewed annualy provided that all the maintenance requirments have been carried out.
The C of A has nothing to do with the annual check what so ever.
THe ARC is normaly renewed at the annual check but it is not unusual to find ARC renewal out of phase with the annual check.
I hope that is clear enough!