I'm currently in the United Arab Emirates, and I am wondering if Etisalat or the UAE can track what I am doing if I use the ZenMate VPN addon to Chrome?
Technically, if ZenMate is considered safe to use, then cannot see the communication.
Etisalat, like any other ISP, will see that you made a VPN connection to a particular service. If ZenMate has no privacy issues (leaking of meta data, DNS queries, you installed backdoored version, ...), then an ISP will not know what data you're sending and receiving over the channel. Which is the same as any other end-to-end encrypted tunnel.
UAE ISP's however block several websites and services that clash with their (perhaps vague) policy, and this is backed by the UAE's cybercrime law; bypassing controls to access blocked content is against the law, but then it becomes a legal issue and this wasn't the question.
Also, as mentioned above, you should really look into the privacy of the VPN in use. You use ZenMate, it is known about ZenMate that it is in a Beta. Also it's not sure what a plugin in Chrome does to your privacy. It certainly means the country knows you were 'gone' from the internet after a visit to the Google Chrome store ;)