Hi!
There are a few things you can do, if you haven't already:
If your iPhone isn't up to date, update it. The latest software is 9.2.1.
In Settings - iCloud, turn off Contacts and enable it again.
Check your internet connection. If it's slow, there might be problems with syncing the contacts to the iPhone.
In the Contacts app, go to Groups, and drag it down to refresh the contacts list. This should help syncing contacts as well.
Force close the Contacts app: double tap the Home button to show the App Switcher, then slide the Contacts app towards the top of the screen.
Restart your device: turn it off and on again.
Hopefully one of these will help.