No trust this computer prompt

First, if you can, try different leads or a different port on your Mac.

If they still don't work then open the Mac App "Activity Monitor" (search for it with cmd-space)

Check that it says "All Processes" in the top LH corner (see image below). If it doesn't go to the menu bar, select View then All Processes.

In the search bar at the top right search for "ampdevice". Select "ampdevicediscoveryagent" in the main pane and then hit the "X" in the tool bar (see image below) then hit "Force Quit" in the pop-up dialog.

Try the iPhone again. If it still doesn't connect then search for usb in the search bar, select "usbmuxd" in the main pane and quit that as above.

If this doesn't work then I'm no help, I'm afraid.

Have you tried turning the phone off and on while it's plugged in to the Mac?

You should also check that you haven't got an update window lurking somewhere on your desktop. You know, the one like this. It might have popped up and you didn't see it or it's behind some other windows.

And, finally, you could try re-starting the Mac in safe mode and seeing if it connects.