Good morning Joni73,
Welcome to the Apple Support Communities!
I understand you have a new iPhone and you are trying to transfer the contacts from your old iPhone to your new one. Can you give us a little more information regarding which model iPhones you are working with and what iOS operating system version you have? Can you see the contacts on your old iPhone? Do you have an iCloud backup of your old iPhone?
Take a look at these resources for setting up a new iPhone:
Set up your iPhone, iPad, or iPod touch
Transfer content from your previous iOS device to your new iPhone, iPad, or iPod touch
Use the steps in this section to back up your previous device in iCloud and to transfer the backup to your new device.
- Connect your previous device to the Internet with Wi-Fi.
- Go to Settings > [your name] > iCloud > iCloud Backup. If you’re using iOS 10.2 or earlier, go to Settings > iCloud > Backup.
- Make sure that iCloud Backup is turned on.
- Tap Back Up Now.
- Stay connected to Wi-Fi until the process finishes.
If your new device needs a SIM card, here's what you need to do:
- If your carrier gave you a new SIM card, put it in your new device.
- If your new device uses the same kind of SIM card as your previous device, transfer the SIM card to your new device.
- If your new device needs a different kind of SIM card than what you have, or if you aren't sure, contact your carrier.
Then use the steps below to transfer your iCloud backup to your new device.
- Turn on your new device. A "Hello" screen should appear. If you've already set up your new device, you need to erase it before you can use these steps.*
- Follow the steps until you see the Wi-Fi screen.
- Tap a Wi-Fi network to join. Follow the steps until you see the Apps & Data screen, then tap Restore from iCloud Backup.
- Sign in to iCloud with your Apple ID and password.
- When asked, choose a backup. Make sure it's the correct one by checking the date and size of each. If asked to update to a newer version of iOS, learn what to do.
- If you purchased iTunes or App Store content using multiple Apple IDs, you'll be asked to sign in to each. If you can’t remember the passwords, you can skip this step by tapping "Don't have an Apple ID or forgot it."
- Stay connected and wait for the restore process to finish, then complete the rest of the onscreen setup steps. If possible, keep your device connected to Wi-Fi and plugged into power after setup. This allows content like your photos, music, and apps stored in iCloud to automatically download back to your device.
If you have iCloud enabled on your old iPhone, then the contacts won't be in the backup. If they appear when you go to www.icloud.com, then that means they are stored in iCloud, and when you enable iCloud and iCloud contacts on your new iPhone, you will see them populate to the new device.
Change your iCloud feature settings
Joni73, please reply when you get a chance with the additional information requested and I'll do my best to help you!