What about the SIM card? Do I have to transfer the current one to the new iphone?

Does the current SIM card have active cellular service on it and do you plan to keep the same carrier, phone number etc.? If the answers are a YES, then you should transfer the SIM card from your old iPhone to your new iPhone so that Cellular service is transferred from your old iPhone to the new one. Ensure that the SIM card size of your old iPhone is the same as your new iPhone.

Axel F.

Depends, if your old phone was a 12 with 5G service and your new phone is a 13, then yes you can transfer it.

If your new phone is a 12 or 13 and your old phone was a model previous to that, the you will want to get a new SIM that can communicate with the new 5G signal.