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It is possible that the application is already open, but not responding. Press Command, Option and Esc keys and this will bring Force Quit window. Select Contacts and click Force Quit. This will close Contacts. Open it. If that didn't work, then restart your Mac.
If that didn't work, then go to System Preferences > iCloud and turn off Contacts option. Wait 2 minutes and turn it back on.
Please let me know if that above options doesn't work, so we can continue troubleshooting