Help!

For Contacts, if you were syncing Contacts with iCloud, have you gone to Settings/Your Name/iCloud, signed in with the same Apple ID, and turned Contacts syncing on? Allow time for the sync to complete.

Contacts, Calendars, or Reminders - Get help using iCloud.     

If you go to iCloud.com/Contacts using a computer browser, do the contacts show there? If they do, try Settings/Your Name/iCloud and slide off Contacts syncing. Wait a few minutes and then slide syncing on. Allow time for syncing to occur.

Last resort - have you tried signing out of iCloud and then sign back in?

Did you review the Apple Support article(s) below?

Contacts, Calendars, or Reminders - Get help using iCloud.     

See Set up your iPhone, iPad, or iPod touch https://support.apple.com/en-us/HT202033 If you followed the instructions found there, then everything expected should be on the new phone.