An animal that is hunting for other animals to eat is called a "predator". The animals that they're looking for are called "prey".

Wildlife documentaries and books that describe animals hunting often use the phrase "in search of prey". It means that an animal is moving around looking for something to hunt down and eat:

Bobcats prefer to hunt along ridges and will follow a ridge for miles, padding silently along in search of prey.

The snake slides along silently through the forest, in search of prey.