I believe you need permission from the CCP to climb there. Permission was granted for the first time ever in 2016, I don't know if they relaxed their stance since then.
In September 2002 I participated in an outdoor climbing comp in Zhangjiajie National Park organized by a regional liquor company. The competition route, protected by a massive toprope, was a steep 60-meter line on some fairly loose rock next to a beautiful waterfall, complete with bolted-on holds at blank sections. There was a ton of local and national media (it was carried nationally on CCTV -- for a few minutes I might have been the most famous white person in China), local government officials, several hundred spectators, and exactly one Yankee. China was a different place then, but just as now, the local people were incredibly friendly and the natural beauty was stunning.