Of course! As long as you have the correct tools and the SIM card is sized correctly for the new-to-you phone, you can absolutely switch it over. By moving your existing SIM card to an older or refurbished phone, you can keep your existing phone number, app and contact data, and stay with your current service provider. However, you should double check to make sure that your new-to-you phone uses a GSM system (which allows you to switch out SIM cards) rather than a CDMA system, which uses an electronic serial number rather than a SIM card to connect your phone to a mobile carrier network. CDMA models won't have a SIM card slot, forcing you to switch numbers, re-download apps, and possibly switch service providers.