transfer sim card to new iphone

Learn which size SIM card your iPhone or iPad uses - Apple Support

Remove or switch the SIM card in your iPhone or iPad - Apple Support

Use 5G with your iPhone - Apple Support

If your new iPhone comes with a SIM card, use that SIM card. If not, use the SIM card from your previous iPhone. In some cases, you need to contact your carrier to set up the SIM card from your previous iPhone for use with a 5G network.

If you plan on using the same cellular provider, and keep the same phone number, then yes, you would install the old SIM into your new phone. One thing is if you want to use 5G cellular, you would have to get a 5G SIM card from your provider.