What kind of data?
If both devices are logged in to the same Apple Account, you can sync data in iCloud like contacts, calendar, Notes and email.
You can also manually download apps from the Apple Account's purchase history.
If you mean a full transfer, like setting up a new device from a backup or "quick start" then no, as mentioned you would need to erase the iPhone 13 and set it up again to use Quick Start or Restore from backup.
Otherwise, if you explain exactly what you are looking to transfer someone may be able to advise.