How to get old messages on your new iPhone

If you were syncing messages with iCloud go to Settings/Your Name/iCloud and turn Messages syncing on. If you weren't syncing messages with iCloud, do you have a backup you can restore from? Restoring from a backup erases all data currently on your device. Any data newer than when the backup was made will be erased. A restore is an all or nothing restore. You can't access a back and only restore certain files.

Backup - Restore your device from an iCloud or iTunes backup.