From Changsha you have 2 overnight trains going direct to Zhangjiajie (02:18 and 03:36/ K536; T8316)
If you leave Nanjing South 15:28 you arrive at Changsha South 21:36 (G 1483).

Or you take the 1st train (G579) from Nanjing at 08:02 in the morning, be in Changsha at 12:52 and take the long distance bus to Zhangjiajie.

Another way is a flight from Shanghai to Zhangjiajie.