Unfortunately, I think @Ultrabenosaurus is right in that you cannot change the time format of the clock. The closest thing that I've found that manages this is under Zorin Appearance -> Interface -> Taskbar Settings -> Position -> Date Menu -> Settings:
While I generally agree that the Gnome developers have gone too far in the incessant pursue of minimalism, this is part of the taskbar itself, so I think it should be possible for Zorin OS to implement a field here to customize the display of the clock. At least, with the layouts that have the taskbar enabled, that is.
In XFCE (Zorin OS Lite) you can right-click on the clock panel -> Properties. There, you can choose between a few time formats, including your own custom one (similar to this thread):