Good evening Paul,
Welcome to the Apple Support Communities!
It sounds like you are trying to see your iPhone 11 Pro screen in QuickTime Player on your Mac with macOS Big Sur.
To do this, you will need to update your iPhone to the most recent version of iOS.
Update your iPhone, iPad, or iPod touch
Then,
- In System Preferences > Security & Privacy, click the Privacy Tab.
- Select "Screen Recording" in the options on the left and add QuickTime Player to the list of applications that are allowed to record the contents of your screen.
- When you attach your iPhone, you will see a prompt asking if you trust the device your iPhone is attached to.
Once this is completed, follow the instructions in the resource below:
Record a movie in QuickTime Player on Mac - QuickTime Player User Guide - macOS Big Sur 11.0
"Tip: If your iPhone, iPad, or iPod touch supports AirDrop, you can record a video on your device and wirelessly send it to your Mac, then open the video in QuickTime Player. See Use AirDrop on your Mac."
If the issue persists, please reply to this thread and we'll do our best to help you!
Take care.