I have installed the CERN override theme, and when selecting it as default, the dropdown arrow on the main menu is not visible. It works when setting the regular CERN them as default. The site is https://cern.ch/test-beams-d8.
I checked the issue you mentioned on a clone website and it is a configuration issue not a theming one.
More specifically, if you navigate to the Block Layout of your website (/admin/structure/block), and edit the Main Navigation Menu, you will notice that the “Number of levels to display” setting is set to 1 (check attachment)
The same setting when you use the CERN Theme is probably set to >1 and that’s why it appears in one case but not in the other. The confusing part of this issue was that when you enable a theme that inherits another enabled theme, the settings of the parent theme are not always inherited and you need to re-set them
I hope this helped, if you need anything else do not hesitate to answer or open another ticket.
Thank you @kplatis, setting “Number of levels to display” to 2 solved my problem as well. It seems that you need to set it to the maximum number of children that one of your parent menu has.
If you want to use the new 3rd level menu, you need to set “ Number of levels to display ” to 3 in order to make 3rd level menu items appear.