To activate an old phone on your current plan, follow your carrier's specific instructions. GSM carriers such as AT&T and T-Mobile require inserting a compatible SIM card, as do LTE phones on Sprint and Verizon. Contact your carrier's customer service to active an old CDMA phone on your plan.
The old phone must be compatible with the current carrier. If the old phone is from the same carrier, the activation is likely to work; for example, an old AT&T phone can activate on AT&T's network without needing to be unlocked. If the current SIM card is not compatible with the old phone, visit a carrier store location for a compatible SIM.
GSM and LTE phones can work between carriers as long as they are unlocked. As long as a phone has been completely paid off and is in good standing with the carrier, it is eligible to be unlocked. While they work between carriers, not all GSM and LTE phones can use their full capabilities on networks for which they aren't designed, due to different carriers using different frequencies and technologies.
CDMA phones cannot be taken between carriers. They must be used on the network for which they are designed due to the specific network technology used. Non-LTE phones from Verizon and Sprint fall into this category.