Get as close to the fence as possible. Use a focusing technique that allows you to focus on the distant subject and not the fence links. I’ve done wolves through a fence with blurred links and it worked OK. The links give a sense of depth and separation.
If you can't get close to the fence, try centering your subject within the openings of the fence. (If you want to meet zoo staff just jump over the barriers and remember to tell them you only wanted to take a closer photo!)
Very good tips have already been posted. They work for me. I will add AF using a single point usually works, but don't hesitate to go to manual focus if your camera is trying to focus on the barrier or the background