Yes, they exist. They take rabbits from contract shooters. Getting properties to shoot is likely to be the biggest hurdle. You would also need about $20k worth of quad, something to pull it with and sundry gear. And a work permit. And a firearm permit.
Best thing would be to come out here on holiday and rock into Tekapo without any expectations. Got to the pub. Shout a few rounds. Ask low key questions but don't be nosey. Someone might take you under their wing. Or you might get punched. Its probably worth the risk.
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