Put my SIM card in an unlocked phone

I am not in a position financially to purchase a "New" phone.  Can I purchase an old model (same as what I have now) that is unlocked and put my current SIM card in it?  My current phone is an S8 that has no battery life left.  I took it in to have a new battery installed, but they told me it was the motherboard that was bad, not the battery.  

I found a place that sells new & refurbished S8's that are unlocked, but I do not know if they will work on the Xfinity network.