This is with a fresh installation of Ubuntu 18.04 using the default GNOME Desktop.
The "tray icons" simply don't appear in the top panel. "Ubuntu appindicators" shell extension is active, but doesn't show any icons.
I've tried both the "kstatusnotifieritem" and "topicons" shell extensions without any success.
If anyone could help I would appreciate it.
Best Answer
What I did was:
Then you can enable either the TopIcons Plus or Ubuntu AppIndicators extension
Reboot the system or instead you could just reload the Gnome Shell with Alt+F2, then R.
Then you would be able to see the icons on the GNOME's bar.