There actually is an aquaponics( I just found out about it recently). It is a hydroponics element to it, but the water that is feeding the plants comes from a reserve that houses the fish. So its kind of a symbiotic relationship. The plants roots help filter out the water for the fish, and in turn the fish food, waste... feed the plants. A friend of a friend who teaches at a high school actually has a whole set up going for his students. I was supposed to go check it out, but things fell through , and the school year ended. Also, bringing strangers on to school property is not as easy as it used to be, so there was a security issue. I have another acquaintance who bought a simple ' at home ' kit for her kids to experiment with. It kinda fits over a fish tank, and grows a small variety of herbs. In either case, it was more for the veggies and not to harvest the fish, but Im sure there are much more elaborate systems that can do both.
It's actually kinda cool and in afterthought, makes a lot of sense since many fish waste contain a lot of nitrogen, which the plants love.