Nokia Lumia 510 - I am thinking of buying a Lumia phone, will I need to get a new SIM card for this device?

You will be advised to change your SIM card either to a micro-SIM or a nano-SIM, which means you will have to contact your operator to order a replacement SIM if a SIM transfer is not available at the retail point. For more details about SIM card, refer to your phone user guide.

Connection problem with the phone may occur e.g. if a regular SIM card has been cut to a smaller SIM format and the card is not sitting tightly in the SIM slot. You should use only proper SIM cards in your phone, do not use SIM cards that have been modified to fit the SIM slot.