What would happen to a food chain if there was an increase in the hawk population?

Hawk prey would decrease, and hawk predators would increase, making hawks decrease again. So to put it in context... Hawks eat mice, right? So the mouse population would increase, meaning more food for other animals that eat mice, like owls. So the owl population would increase, making mice decrease. Then animals that might eat hawks (I don't know if anything does) would increase, and eat all of the hawks then everything would eventually even out again.

To answer your question, lots of things will happen, but it will all even out again.