See regulations here: Nps.gov

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.