Two issues here. Firstly you need a ships radio licence to have to radio on board and then you also need an operators certificate. You will be required to do a one day course on VHF voice procedure and also how the DSC system works. I would guess that because you have asked the question you do not have the operators certificate.
Ok, so just inform Ofcom that you have now got a DSC radio and that you now require an MMSI number. Your existing call sign will remain unchanged as will all the other details.