Don't need. The Police officer in NPC/NPP will paste a sticker with the new address over the old address on the NRIC. Other than that, need to watch out for those that did not have any connection with ICA as your address will not be update to their database (like insurance, bank etc)
any NPP can do it liao. Its one stop services. CPF, income tax, etc all updated at one location. I had done it 1 1/2 years ago. They will stick yr new address on yr IC, DL and also for yr CAR log book. Took less than 10 min.