When I was in college the biology department got donated half of a lion for dissection by veterinary students. We got the back half. I feel like that said something significant about the quality of my education.
I think I remember some years ago a zoo fed a dead giraffe to the lions and people went absolutely insane about it. I'm not sure about the details anymore, they might have killed it because there wasn't enough room in the zoo for it? Either way I didn't get it, what do they think the lions are fed any other day? Animals that weren't killed explicitly to become food? Some cows that couldn't bear existence on this world anymore and offered themselves as lion food? Where is the difference?
A local zoo has a "taxidermy department" and noteworthy animals are preserved or skinned and the skins sold to friends of the zoo.
Its kept very secret because it would be publicly unpopular. A friends dad has a mountain lion skin because he is a contractor who does a lot of work for the zoo and did a few jobs for them that NEEDED to be done basically for cost when they were suffering some financial troubles. They gave him the pelt as a Xmas present.
One day, a patrol car in the Bronx finds a headless body laying in the street. The victim's hands, feet, and skin was removed. There's a massive response to find the deranged killer. Everything gets called off in a few hours, after the coroner realizes that it's the body of a gorilla.
What do you do if you have a horse that dies or has to be put down? You call your neighbor down the road who has an excavator and ask him to dig you a horse sized hole. Then you bury it. If you don't, you won't want to leave your house for at least a week.
My zoo buries them on the premises. I know of a camel, a moose and a few other things got buried there. They have a large plot of land that is used to dispose of organic waste like branches and trees, old compost, etc until it's full and needs to be tricked out to the landfill. They just bury the animals under the ground there.
In college, I got a job on campus in their Environment, Health, and Safety department. Mostly, I just calibrated fume hoods in labs.
During my time there, a hippo at a nearby zoo passed away. I don’t want to be too specific because it can be a bit icky, but they essentially shipped it to us for incineration.
If the animal was healthy when it was alive and if it's big enough, I believe they butcher the carcass and feed them to the carnivores. ~~I remember a news story about a recently deceased giraffe was fed to the lions in the zoo. ~~
I was wrong, the giraffe was killed to prevent inbreeding.