I understand that you have an app that needs to be updated, but when trying to do so in the App Store on your iPhone, the option to update it is not available. I'm happy to provide some help for this issue.
I recommend that you force the app that you're having this issue with, as well as the App Store, to close. Once those are closed, restart your iPhone and attempt to update it again:
How to force an app to close on your iPhone, iPad, or iPod touch - Apple Support
Restart your iPhone, iPad, or iPod touch - Apple Support
Thanks for using the Apple Support Communities. Cheers!