I work remotely for a company 16 hours ahead so would like both dates and times at the top if possible. Is there any way without opening an app or a dropdown box? Just always displaying at the top. I am on a Lenovo Ideapad 3, Ubuntu 20.04 LTS and is the pic below indicative of gnome desktop? I am not too familiar with the names. I just use the default that comes with each distribution of Ubuntu LTS's.
I think the Panel World Clock extension is exactly what you are looking for.
It will display the times for the locations you have setup in the Clocks application, directly in the topbar. You can configure how many of your configured time zones are displayed.
To install the extension, you will need the GNOME Shell version. You can check this by opening the System Settings app. Select About in the left pane, and look for GNOME Version in the right panel. Alternatively, on the command line, you can execute
dpkg -l gnome-shell to get this information.
For Ubuntu 20.04, the GNOME Shell version is 3.36.
Setup your time locations in Clocks, and the Panel World Clock will automatically pick them up.
Clocks is not installed by default in Ubuntu. For this extension to work, you must have the Clocks (a.k.a. GNOME Clocks) application installed. If you already don't have it, you can install it using
sudo apt install --no-install-recommends gnome-clocks).