Is the new Galaxy phone purchased as part of a Fixed Term Phone Contract or is it Pay-as-you-Go?
Likewise, is the current phone on contract or not and what model type is it?
If the new Phone is purchased as 'Unlocked', that is not locked to any particular phone service provider, and your current SIM is not fixed to any specific phone contract, then you should theoretically be able to fit the old SIM into the Galaxy and continue as before. Thats also assuming the SIM from the current phone is the same type / physical size as the Galaxy SIM.
If the current phone SIM is the same size as the Galaxy, you can always try it in the Galaxy as it should not cause any issues other than it may refuse to work!