You could try a Forced Restart, when issues develop following an update it may sort some of them out, a bit like booting into Safe Mode on the Mac.
Force restart iPhone - Apple Support
The next option is “Reset All Settings” under Settings>General>Reset, you will not loose data or content but it puts the iPhones settings back to default.
If that doesn’t work you can try removing and then re-add the Contacts App.
The Contacts App should be available in the App Store so if you delete the one on your iPhone you should be able to reinstall, just search in the App Store first to ensure you can find it.
If you are ok with the above it’s important next to confirm how your contacts are managed, if synced via iCloud you can turn that off first under Settings and then delete the Contacts App.
Keep your contacts up to date on all of your devices with iCloud - Apple Support
Restart the iPhone then re-download the Contacts App, after which turn on Contacts under iCloud settings.
The process of removing the app can clear out associated files that may be causing issues.
If you don’t use iCloud to sync your data I would suggest you turn it on first before doing any of above, if not you will be relying entirely on an iTunes or iCloud backup.
The first two are fairly straight forward, but deleting the app comes with risk so make sure you have a backup of the data in some form, even if that’s in hard copy so you can input it back again by hand if necessary.