I'm not sure what you mean here. If you downloaded mSecure onto your new iPhone 14, then all you need to do is sign in to the same account on your new phone. You'll use the same email address and password that you used in mSecure on your old phone. Your account's password hasn't changed, and mSecure isn't keeping from signing in.
With regards to Face ID, whenever you set up a new device, the Facial data has to be set up from scratch, and the app data that was stored behind Face ID on your old phone is never transferred over to the new device. You can't use Face ID to open a security app like mSecure after new Facial data has been set up on a device, like you did on your new phone. That's just the way Face ID works, and there's no way to change that. For apps like mSecure, you have to download them to your new device, sign in to them with your password, then you can enable Face ID for future use.
Real quick, do you still have access to your old phone? If you do, the fix for what's happening is very simple.
How do I cancel MSecure?
Thank you for contacting us. I can help you with cancelling your mSecure subscription, but I did want to let you know I'm here to help you with any issues you may be having. Have you run into a problem while using mSecure? If so, I'm sure I can help resolve whatever the issue is pretty quickly.