iOS Spotlight searches displays really old contacts as tophits

I experienced a similar glitch with iOS 10 as well.

The only way to clear the Spotlight searches without using third party apps is this:

1. Make sure you're running the latest iOS (Settings > General > Software Update).
2. Force restart your iPhone (hold the power + home button until the Apple logo appears. iPhone 7 (Plus): hold the power + volume up button).
3. Disable Spotlight: Go to Settings > General > Spotlight Search. Disable "Siri Suggestions", "Suggestions in Search" and "Suggestions in Look Up" as well as "Contacts", "FaceTime", "Messages" and "Phone".
4. Go to Settings > iCloud . Disable "Contacts".
5. Force restart your iPhone once again.
6. Connect your iPhone to your Computer using a USB cable and create an encrypted backup with iTunes.
7. Verify that the backup was created successfully. Look for a phrase like "Last backup: 10:23 AM").
8. Restore your iPhone. Select your device on the left side in iTunes and press "Restore...". You may need to remove "Find my iPhone" first to continue.
9. Wait for you iPhone to reappear in iTunes.
10. Select "Restore from backup" and choose the backup you created in step 6.
11. Wait for iTunes to finish restoring your backup.
12. Re-enable the settings you disabled in steps 3 and 4.

Please let me know if this works for you.