On macOS 12 or earlier, if the Clocks palette doesn't appear at startup despite you selected the "Always show palette at startup" checkbox in the Palette pane of World Clock Deluxe Preferences, the World Clock Deluxe application is probably hidden after it is opened automatically.
Open System Preferences, and then click Users & Groups.
Select your account and click Login Items.
Make sure World Clock Deluxe has no checkmark in the Hide column of the list.