How to backup phone contacts before getting new phone

Yes. How to back up your iPhone, iPad, and iPod touch - Apple Support provides backup instructions.

Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support describes how to setup your new "phone."

Here is How to back up your iPhone, iPad, and iPod touch - Apple Support

You’ll want to have a backup, regardless.

Devices can get lost and stolen, and devices can be damaged or can fail, and the backup is your path to recovery.

If your contacts are stored in iCloud and not locally, then your contacts are stored in iCloud and cached locally.

Here is how to Set up and use iCloud Contacts - Apple Support