The New Shadow refers to an abandoned manuscript. J.R.R.Tolkien wrote about the coming of the "Dark Tree" which was an abstract concept that described how deep evil's roots were in the planet and middle earth. The New Shadow itself could possibly be seen as Herumor--but this may be unlikely as the manuscript seems to talk about Herumor as being the leader of a cult and the manuscript seems to denote someone else as the "New Shadow." Who this is or was intended to be...we may never know as possibly Tolkien himself was unsure and abandoned the concept.
The Advent of a new shadow might correspond with biblical apocalyptical literature, for example the book of revelation, which mentions visions of false prophets, demonic beasts and the coming of the Antichrist.