Kids at the age of 15 and below do not have to be licensed—special licenses for certain species are still required. Everyone else that is above that age should get a license in order to hunt or fish.
Senior New Hampshire residents can get licenses at a discounted price. To qualify, you need to be 68 years or older.
If you are a non-resident, confirm that you are eligible for the license you want to purchase. Some are only given to NH residents.
To get your license and/or for more information, check out the Fish and Game website.