See regulations here: nps.gov/neri/learn/m...

Details:
__b___(3)_ Trapping

A. Trapping is specifically mandated by Federal statutory law within the Gauley River National Recreation Area_GARI_and the Bluestone National Scenic River __BLUE__.

B. Trapping in prohibited within the New River Gorge National River __NERI__.

Justification - Trapping within the Gauley NPS areas is allowed under the parks’ enabling legislation. Trapping on the Bluestone National Scenic River is allowed under the state license agreement; trappers must be registered with the Bluestone Wildlife Management Area Department of Natural Resources manager pursuant to WV state law.