Thanks. Let's try this:
On your Mac, open System Preferences and choose iCloud.
Turn OFF Contacts by removing the check mark. If it asks whether to leave contacts on the Mac, say NO.
Close System Preferences.
On your iPhone:
Turn Contacts OFF. If it asks whether to leave contacts on the iPhone, say NO.
Now, on your Mac, log into https://www.icloud.com/
and open the Contacts there.
Click the gear icon in the lower left and choose "Select all"
Click the gear again and choose "Delete".
When it has finished, you may close the browser window.
Now, try re-enabling iCloud first on the Mac and then on the iPhone.
After a few minutes, see if contacts successfully sync from Mac to iCloud to iPhone. You may need to restart both Mac and iPhone once if you don't see immediate results.
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