There is no information available to suggest when the mythical next version of NetHack will be released, other than "When it's ready." 
After the release of NetHack 3.4.3 in 2003, the NetHack DevTeam went on a long hiatus. 3.4.3 was long considered by some to be the final version of NetHack until December 8, 2015, exactly twelve years after this version's release, when NetHack 3.6.0 was released.
Leaked 3.5.0 source code
In September 2014, a leaked source code distribution described as "NetHack 3.5.0 Beta" was circulated on the Internet, e.g. in the Usenet newsgroup rec.games.roguelike.nethack. In response, the DevTeam posted an official announcement on nethack.org confirming the leak, but refuting any claims that it would represent an official release (beta or otherwise), and also retiring the version numbers 3.4.4 and 3.5, which had been incorrectly associated with the leaked code:
Recently a NetHack source distribution has appeared, claiming to be NetHack 3.5 or 3.5.0 or 3.4.4.
This claim is partially correct. This is our code. However it was not released by us or with our authorization. This code is not ready for release: it is unfinished, unpolished, and almost certainly very buggy. It has not been play-tested for balance or functionality. It is best considered a partial and unfinished rough draft. We will not be supporting this code, nor will we be releasing binaries or bugfixes for it. It will not be available through our website.Due to this incident and to prevent confusion, we will not now nor in the future release anything with a version number of 3.4.4, 3.5, or 3.5.0.
Discussion about this leaked code can be found in the article leaked development version.
NetHack 4 confusion
There is a variant of NetHack called NetHack 4 but it is not actually the official/vanilla version 4 of NetHack from the DevTeam. To clear up this confusion, the DevTeam internally refers to that variant as NetHack4, without a space between "NetHack" and "4". The latest version of official/vanilla NetHack is currently 3.6.0 but it does incorporate some code from NetHack 4 as well as several other variants such as UnNetHack according to its release notes. Anyway NetHack 4 is a fork/variant of NetHack with additional features but it is not actually version 4 of NetHack. There is currently no official/vanilla version 4 of NetHack although it might be possible in the future.
- NetHack 3.6.0: Known bugs — What will be fixed in the next version