I’m not a lawyer, these are just common sense advice.
Can you publish and use photos you’ve taken in a zoo and earn money from the photos you’ve taken in a zoo?
Ask the zoo in advance, preferably send them an email so you’ll have it in writing, and save this for later.
Most zoos are privately owned and may have different views on the professional use of photos taken in their zoo. Quite a lot of zoos are happy for the extra attention they’ll get from your work, but don’t assume. Some countries have different rules than your country, so when you travel, be extra alert. Again; ask in advance, or if it’s a spur of the moment ask them after
Another thing to be aware of is that not all stock agencies accept photos of animals shot in a zoo.