If you want to summon a creature to hunt, then I suggest Summon Extra Planar Creature instead. The options for summoning are much more varied, but also much more random.
Also, note that what you summon is sentient (either Extra Planar Creature or Magical Creature). You will need to bargain with what you summon to perform a task, and typically these types of creatures like magically attuned objects such as Reagents, Catalysts, and other items that have a magical resonance; sometimes they want mundane objects such as coin. Additionally, based on the task and/or payment, there may be additional restrictions imposed such as forcing the Ritual Caster to occupy the summoned creature's place on their native plane.
Unless you are dealing with a noble being, be mindful of trickery. You want to be explicit in your bargain/task. A request to engage in a hunt could, depending on the power of the creature, be disastrous or wonderful based on how the hunt is defined. For instance, if not worded properly it may hunt you instead of the other way around.
At least with a summoned creature there is no death; a dead summoned creature just goes back to it's home plane (no body to feast on), albeit painfully and potentially weaker, but generally intact.
Regards,
Alavatar