The purpose of the hook grip is to make the grip on the bar more secure, allowing a better force transfer to the bar.
As such it can be used when doing any type of pulling (cleans, snatches, high pulls, deadlifts, I even use it when doing heavy rows). You don't HAVE to use it, but it does help pulling big weights explosively.
With high pulls, you can use straps though.
For clean and presses don't worry about unhooking after the clean, it will happen by itself when you rack the bar.