Yes. The old SIM is micro while the new one will need to be Nano (smaller)
That said, its possible the old SIM already has a Nano SIM punched into it (these days you just get sent a single big SIM and you punch out the form factor needed.) So pop out the SIM and see if it has the ability to press out the smaller size.
All SIMs are actually the same in the middle. They're just surrounded by plastic to fit the slide. Its actually easy to just cut the SIM you have down to the size required as shown here