Hello!

I am using Zorin OS 16, Ubuntu based with Gnome desktop. My computer display is a large TV screen rather then a monitor. When my system sleeps, the display does not gracefully turn off, and it will not turn back on when the system wakes.

The display does not have very good ip-control but does support hdmi-cec. As my video card does not support cec, I've used an cec injecting adapter and can send on and off commands from the terminal.

What I can't figure out how to do is get the system to send the on/off when it wakes or sleeps the monitor. Is there anything in Linux that listens and reacts to system events like that?

It pays to be specific in your terminology. "sleep"is a term usually associated with monitor(s) - at least in my case.
Presuming you are actually referring to system suspend/hibernate, there are various options depending on power management agent in control. The Arch linux wiki is an excellent resource for all things Linux - have a look at this page - the bit under sleep hooks is what you are after.

udev (more-or-less random link, there's other introductions to udev around the web)