Hey cathy8_4,
Welcome to Apple Support Communities. Sounds like you're needing help setting up your new iPhone 13. We'd be happy to help out.
To get started, if you didn't activate the iPhone with your carrier during purchase, then you'd need to move the SIM from your old iPhone to the new one. One thing to keep in mind though, is if you're coming from a 4G phone (anything prior to iPhone 12) you may not have a 5G SIM card in your old iPhone. Therefore, you may need to reach out to your carrier for help with activating the eSIM (built-in electronic SIM) or else getting a new 5G SIM card if you don't have one already.
Once this is complete, you'll definitely want to get your new iPhone fully updated. If you have trouble doing so during setup and need it in order to restore a backup, you can always set the phone up as new, get it updated using the Settings app or a computer, and then erase the phone and attempt the setup and restore from backup a second time. For help updating: Update your iPhone, iPad, or iPod touch
For more info on activating your iPhone, as well as setting it up and transferring data, check out these resources:
Set up cellular service on iPhone
If you can't activate your iPhone
Set up your iPhone, iPad, or iPod touch
We hope the information and resources above help out with resolving your issue.
Take care!