If the purpose here is to document the head shot and partial back hair of a whatever it is deer, than you have done that. My first comment would have been to shoot this type of close up in portrait orientation, or back way out and give him lost of room on one side or the other.
If ever I shoot animals that have tags or collars - and there are wild ones that do have them, I decide right up front whather their environment and their jewelry are important, if not, I try to shoot them doing things that show action, but DO not expose their tags – unless I’m doing some kind of documentary on the animal itself then the tag and the pen they are in become critical. You can choose to use their environment to your advantage or not.
This happens to be one of the main reasons most of us like to be told of captive shots (sometimes its easy to fake a captive into a wild shot).
There are limits to what you can accomplish in a zoo, on the other hand, zoos alow you to control the environment and to some extent the animal, you can get close, and youre safe.
Unfortuately, if time is critical, you have to wait until the animal is in a position or a place that will allow you the most optimum shot, even if that means you have to go back 5 times, or sit there for two hours or more.
It happens to me all the time, only I'm chasing wild ones with no fences but the point is I've waited days and spent lots of money on travel only to come home with a goose egg because the light was wrong, or the animals were not around or whatever. Today I waisted two hours and came home with negative 10 bucks in gas. . .
So, I don’t know how much more I can tell you about that shot since the limitations of it are what they are.
That said, here's one example of how I might try to go tight on him rather than letting the fence push my framing. It's a full frame crop, that still shows the distinguishing characteristics of this animal, (back hair, eyes, face, and big ears) but looks planned and thought out.
Your shot was forces because of the constraints of the zoo and you let that tell you how to shoot this animal. Keep in mind, you may have to sit there and wait for as many hours as it takes to get the shots you want, if you don’t have time for that, force it like I did. . .
Cheers . .
Ps, I also did a little ps work on it. . .