Hi AndyMiller1989,
We understand tapping message in a contact card does not bring you to an existing message conversation thread.
We would recommend ensuring the contact card has all relevant contact details such as phone number and email address that may be used for iMessage.
If the issue persists, we would recommend ensuring your software is up to date. You can learn how to do so here: Update your iPhone, iPad, or iPod touch.
If the issue persists further, we would recommend ensuring you have a backup of your data (How to back up your iPhone, iPad, and iPod touch), then Restore your iPhone. You can learn how to do so here: Restore your iPhone, iPad, or iPod to factory settings.
Once complete, Setup As a New Device (do not restore your backup).
If the issue is resolved, go ahead and restore your backup. You can learn how to do so here: Restore your iPhone, iPad, or iPod touch from a backup.
If the issue recurs once your backup is restored, there may be an issue your user data, in which case we would recommend you sync your content to a service such as iCloud, then erase your device and Setup As a New Device - all synced data will return, though you will need to re-download your apps and adjust your user settings to your preference.
Hope this helps!
Thank you for using Apple Support Communities.
Cheers!