While "outfitter" is a good starting point (outfitter: a business that provides equipment, supplies, and often trained guides for activities such as hunting, hiking, etc.; also : a guide who works for such a business, http://www.merriam-webster.com/dictionary/outfitter), but the term doesn't seem to cover the management of hunting grounds.


Ana Vozone's definition (see Reference Comments) leads me to think that we're dealing with one of the following:


hunting farm / commercial hunting farm
http://shorewindshuntingfarm.com/index.html
"comercialización a través de la venta de cacerías": http://www.shorewindshuntingfarm.com/daily_hunts.html
http://www.gamecreek.com/
others https://duckduckgo.com/?q="hunting farm"&t=ffab&ia=web

http://www.ombujomenge.com/hunting-farm/ , a site from Zimbabwe mentions "farm-manager" as job title. In American sites, evidence abounds that "hunting farm manager" is a job title. (A sampling can be found at https://duckduckgo.com/?q="hunting farm manager"&t=ffab&ia=w...


game reserve (UK) / game preserve (US)
def.: a large area of land where wild animals are either allowed to live safely or to be hunted in a controlled way for sport
http://www.macmillandictionary.com/dictionary/american/game-...
Wikipedia adds "Many game reserves are located in Africa. Most are open to the public, and tourists commonly take sightseeing safaris."
(A company called Safari XXX is mentioned in the context.)
https://en.wikipedia.org/wiki/Game_reserve
Again "game reserve manager" is the job title. https://duckduckgo.com/?q="game reserve manager"&t=ffab&ia=w...


hunting preserve
This term also appears, with one example among many being http://mountainmeadowhunting.com/MountainMeadow_About.html


wildlife management companies
These appear to act more as consultants or real estate agents, but some overlap may exist with hunting farm management.
http://westerveltwildlife.com/
http://www.mumwildlife.com/
http://www.americanforestmanagement.com/Wildlife_Management-...
http://orionwildlife.com/
http://www.southernheritageland.com/services/wildlife-manage... (The landowner will be able to hike, hunt, picnic, fish, relax, ride ATV’s, camp, and leave the forestry and wildlife management work to SHLC’s team of professionals who will create a productive, working forest... [bold mine])

To hunt on wildlife management areas (WMAs), you must possess a management area permit and a hunting license, (and often other permits depending on species and season), unless exempt. Limited entry/quota permits are required on WMAs during certain time periods. They can only be applied for during the scheduled application periods. The worksheets with the hunt choices and hunt dates are usually posted about two weeks before the permit application period opens.
http://myfwc.com/hunting/wma-brochures