You get free entry to New Jersey State Parks and Forests as a resident New Jersey National Guard member who has completed initial active duty training, or as an honorably discharged resident veteran with a service-connected disability rating.
There is nothing to apply for. Show your proof of eligibility at the park entrance. For questions, call the New Jersey Department of Environmental Protection at 866-337-5669 or 609-777-3373, or use its online contact form.
Your National Guard ID and proof you completed initial active duty training, or your DD214 and VA disability rating documentation, plus proof of New Jersey residency.