The first time you try to use Face ID for an app a system permission alert prompt is shown "Do you want to allow to use Face ID" (like Photos, Contacts etc permissions). However, there appears to be no way to reset this.
I've tried deleting the app and re-installing, and even resetting Face ID on my phone. But once I re-install the app the Face ID permission is already enabled for the app in Settings -> Face ID and in Settings -> <app>, and when I attempt to use Face ID it works right away, without the permission prompt appearing.
Seems like a bug. To be clear, this is an app I'm running on my iPhone X via Xcode, not an App Store app (I don't know if that makes a difference, it shouldn't).
Using a new Bundle ID each time to test this seems a little drastic š®
If you go into Settings > General > Reset > Reset Location & Privacy this resets the Face ID permission alert.