Light is a little harsh and I would have prefered the frame a little higher up (giving a bit more head detail from the animal and a little less deadspace at the bottom) A little more to show the full hand would also help - but overall I do like what you've captured.
As for getting better a few ideas you can work on;
1) Don't take family/non-photographer friends. Not being anti-social, but when you're out and about with people for things other than photography (esp if its with family) then its a lot harder to do what you need to help get those top shots. Instead you'll find yourself focusing on your companions far more; talking and interacting with them; heck capturing shots of them. That is no bad thing, but if you walk in wanting shots of the tigers then its somewhat distracting.
2) Get in early - zoos tend to open late which makes things more tricky; but getting in as soon as you can has a few bonuses. First up the light will be softer than at midday; secondly you can often avoid the early crowds this way. Giving you a little more room and a little more peace and quite for a while.
3) Plan your trip - have an idea of what animals you want to focus on - this could be anything from following the feed times around (most zoos have rolling feed/attraction events so that you can move around and catch most of them one after the other) through to only going to get pics of one single animal.
4) Scout out the pens - don't just roll up, shoot and move away; spend a little time trying different positions and seeing what else is on offer. Remember sometimes you'll find that the ideal position will be away from where the animals are when you arrive; you either accept that and move location or settle down and wait.
5) Chat with the keepers/staff - ideally when they are not dashing from AtoB doing things - a quick chat can often give some great results and hints; things like a certain animals habbits or general motions around their pen. These can be great little tidbits of info, esp if you don't have the option to return to the zoo time after time to build your own info pool on familiarity with the specific animals.
6) Get up close; not that you must only take close shots, but rather that you get close to any wire/bars/glass screens that you can. This helps since being close to wire helps to blurr it out of vision of the camera; whilst being close to the glass reduces reflections. Sometimes this is more tricky (big cats often have a second further barrier to prevent you getting close enough to press up to the wire (and thus be in range of kitty claws).
7) Seek special benefits - this is more easily done with a zoo you can visit often and is also generally a lot easier with smaller wildlife centres or family run zoos. Asking for favours (keepers are about the best place to start rather than ticket operators) such as getting early entry to the zoo (most zoos start work much more early than the public are let in). This is clearly more tricky are bigger establishments as the staff have more restricted freedoms and the chances of talking to real desision makers is more limited - on the other hand big places often have annual sponcerships and events for those members; joining up is a great way to network and hopefully meet those gatekeepers.