There is no fee to hike. A backcountry pass is required for any overnight camping in the Red River Gorge Geological Area and must be displayed in your vehicle between 10pm and 6am. Passes are $5/day, $8/3 days and $50/year, sold at local stores and the Gladie Visitor Center.
Camping is prohibited within 300 feet of developed roads and Forest Service trails, within 600 feet of Gray's Arch, in picnic or parking areas, and within 100 feet of a cliff base or the back of a rock shelter. Park only in designated areas along KY 77 and KY 715.
Sources: Powell County Tourism – Hiking & Camping · RRG trail map (PDF)