These arguments are also going to be based on a scenario where population control is already being managed via birth control methods.
Here is my list:
1- The biggest reason I see hunting as ethical is it prevents an individual animal from suffering a horrendous death via predation, starvation/disease, or otherwise old age without medical care.
So many of us have watched documentaries growing up where the screen cuts to black when the prey is captured. We don't see them being literally eaten alive. If you spend any amount of time online watching real nature videos, you'd know that a bullet is a much more compassionate death. Even if it misses the mark, they aren't full of horror from being chased and mauled, and the hunter will do everything possible to make sure they are dispatched quickly.
2- Hunters have the ability to target specific aggressive individuals who are causing stress to the group or who are hoarding resources/mates. This can include older dominant males for example, who have had years of successful breeding already. It gives the younger males a chance to step up and relieves their stress, on top of saving them from injury from a fight. And it gives the older male a quick and more dignified death compared to what he'd experience down the line when he loses his throne and gets eaten alive.
3- Protecting herd health. Hunters have the ability to kill animals showing signs of disease or genetic abnormalities, keeping them from spreading throughout the herd. Yes we could develop vaccines and possibly treat certain diseases in a way that doesn't involve killing, but this is an alternative when those options aren't available.