A handful of hunters will soon be permitted to bag an animal rarely hunted in North Carolina: an American alligator.

The state’s Wildlife Resources Commission will allow alligator hunting in Hyde County beginning Sept. 1, marking the first sanctioned hunt in the state in more than 40 years. So far, demand is high, with more than 400 people applying for 20 permits, said Alicia Davis, a conservation biologist at the commission.

The...