How do I re-authorize Quicktime Player to use the microphone when once it has been denied?
Go to System Preferences > Security &amp; Privacy > Privacy > Microphone, unlock the preference pane by clicking the padlock symbol at the bottom left of the window and tick "QuickTime Player.app", which should be listed without a tick mark in its checkbox.

If QuickTime Player.app is missing, you should be able to reset all decisions you made for the various applications that asked for access to your Microphone by quitting System Preferences, opening Terminal (to be found in /Applications/Utilities/, or search via Spotlight) and running the following command:

tccutil reset Microphone


...then press enter.

This should clear all applications from the Microphone section and after launching QuickTime Player, it should ask for permission to the microphone all over again.