The Advanced pane of World Clock Deluxe Settings (macOS 13 or later) or World Clock Deluxe Preferences (macOS 12) lets you open World Clock Deluxe automatically and hide the Dock icon.
Open World Clock Deluxe automatically
Select if you want World Clock Deluxe to open automatically when you log in to your account. The World Clock Deluxe application will be added to your login items.
Hide World Clock Deluxe icon in the Dock
Select if you want the World Clock Deluxe icon not to appear in the Dock.
When the icon in the Dock is hidden, World Clock Deluxe has no menu bar. To open windows, view the Help, or quit the application, use the World Clock Deluxe status menu towards the right end of the menu bar.