NetHack: The Next Generation was Sebastian Klein's variant of NetHack 3.1.3. Its main features are Geek as a new role, and various monsters and jokes borrowed from the works of Douglas Adams.
The documentation also describes a feature that allows players to reroll new characters. They may even specify minimum features! This is normally something that we expect of Angband, not NetHack.
NetHack TNG has become obscure, as apparently no one has bothered to port it to newer versions of vanilla NetHack. Though Sebastian Klein's original distribution site is missing, J. Ali Harlow offers NetHack TNG (in the form of a patch from the 3.1.3 sources) on an archive site.
However, TNG seems to be more popular among Japanese players. Apparently TNG was ported to JNetHack, resulting in "JNetHack-3.4.3-0.8-TNG".
Anglophones may be noticing NetHack TNG again now that Edrobot is using it as a vehicle to put Douglas Adams jokes into Dudley's dungeon. The story arc begins at 24 April 2007; NetHack TNG becomes a plot twist at 1 May 2007.