Of course.
In 2015, four South Island Takahē were shot during a Pūkeko (Australasian Swamphen) cull on Motutapu Island. The cullers were hired by the Department of Conservation and were members of the local deerstalkers association. The cullers were informed of the differences between Takahē and Pūkeko before the cull started. It appears highly unlikely that the cullers were prosecuted.
Pukeko culls halted after endangered takahe shot - NZ Herald
Relief as DOC takahe killing case ends
In 2018, a man killed nine Red-billed Gulls. The man was sentenced to community detention.
Driver sentenced for killing red-billed gulls at Kaikōura wharf
In 2018, a man killed a Kea because the Kea was being noisy. The man was sentenced to 150 hours of community work.
Man sentenced in Nelson for killing a kea
In 2018, a dead Weka that was claimed to have been killed by ingesting 1080 poison was discovered to have actually been shot. It appears highly unlikely that any prosecutions were made in relation to this incident.
Weka dumped at Parliament by anti-1080 protesters was shot, autopsy says
In 2020, a man was filmed stabbing a New Zealand Fur Seal pup. It appears that the man was not prosecuted.
Sickening video shows man stabbing baby seal in Kaikōura
Man's charge following seal stabbing video amended
Also, New Zealand Birds Online includes this sentence in its page for the Grey Teal:
From what I can tell, prosecutions for the killing of Grey Teal in New Zealand are extremely rare, so how can the Grey Teal honestly be called a species that is protected from hunting in New Zealand?