SIM CARD

As Chattanoogan, stated, the SIM will work but is not a 5G SIM. If you need to use it while until you get in touch with your carrier it should, however, be fine. I would point out that there is nothing on the SIM to back up. All a SIM stores on an iPhone is the carrier information. But, you should always keep your phone backed up!

Note that while your old SIM might “work” it’s certainly not provisioned for the 5G services for which your “13” is capable.

So … since you need to contact your carrier anyway, suggest you use this opportunity to update to an eSIM if it’s supported by your carrier.

See more background info here:

About eSIM on iPhone - Apple Support

Hello!

If your cell service is working properly with the new SIM, then there should be no need to go back to the old one. If your service isn't working right, you may need to try the old one. You can also visit your local carrier store to have them check it out. I cannot provide specific instructions as I do not know who your carrier is!

CF

Disclaimer: Information may not be 100% accurate as I learn new things every day!