SIM card compatibility
Can I use my NANO SIM card from my iPhone XS in my iPhone 13 Pro?
iPhone 13 Pro
Question marked as
You can and it will work just like it does in your XS.
BUT …
However, to use the 5G capabilities of your 13, you’ll want to get it reprovisioned by your carrier.
This might be an opportune time to have your carrier provision your 13 with an eSIM.
(and depending on how you purchased the 13, it might be already)
About eSIM on iPhone - Apple Support
and
Transfer or convert your current SIM to an eSIM on your new iPhone – Apple Support (AU)