Right-click the Unified bar (the one with the search box), Customize..., drag the Address Book icon onto the bar, Save.

Right click on Unified Bar does not offer "Customize"

See attached picture. Or, click the 3-bar AppMenu icon, View, Toolbars, Toolbar Layout.

OK, I now have the icon. what bothers me is what happened to it. This is not the first time that it moved from it's usual place that I had been using if from for years. I think it had resided on the menu bar back then. Was it by Mozilla design that access to the Address Book was hidden from view or something wrong with Thunderbird on my machine.

My machine! I booted up an extra machine and saw that the icon showed up on the strip on the left of the screen (Spaces Toolbar) Looked at view and saw that it was enabled. Was not enabled on my daily driver. Enabled Spaces Toolbar and Address Book icon showed up in it's usual spot. Had a power outage the other day that might have caused some disturbance.