As I understand it, the EASA Standard CofA is issued to all EASA aircraft now. At that time you state whether or not you want to do aerial work (old Public Cat).
If you do you get a Certificate (of Release??) from the maintenance organisation, If not you don't. Any instructor will want to see this beforehand as he won't be allowed to charge for his time without it.
To get the certificate, the maintenance organisation may well want to reinspect the aircraft before issuing the new certificate, although that might depend on how much they know about the aircraft.
Of course, if you do upgrade, then you fall foul of the new engine time regs, so it might not even be possible if your engine is on condition, or if it has tripped the calendar life.