Maybe we could place traps to ensnare wild animals?
A trap gets placed in the wild, after a certain period of time... you may get an animal based on the size/type of trap used. This would be over a good few hours, and takes time to set. So cant be used to chase a rabbit into it (that would make things too easy).
So with the normal hunting skill at low level. you get make small snares for rabbits and squirrels. As well as a trap for frogs/toads or even insects (food and curios). This would use basic string, some twigs maybe a stone, bark.. whatever, low level foraged stuff.
As you get more trapping skills, you can make better traps to get bigger game. So for say a fox of badger you would need higher level materials. But not too high... so blocks of wood maybe plant fibres more stone etc.
For larger game, metal would be needed as well as knowledge of mechanics and they would have their own specific traps.
When catching bigger game, there is a chance they could be dead... or just wounded to the point where they would run away. If say for example, its a boar and not a badger as you wanted... you can just open the trap and the boar will run (as its HP is at that flee stage). If you choose to fight it, it cannot flee as you have not released it from the trap.
The trap is used up in this process, and its quality affects the quality of the animal caught. if a trap of the same type/size is placed within X distance of another, its chances of success is reduced.
You could also place fishing traps in shallow water. Leave them for a few days and see what you get. Naturally, if every trap gave a kill/catch then it would be too easy to do, so an appropriate balance would be needed.