"The New Shadow" was the working title of J.R.R. Tolkien's ill-fated sequel to his masterpiece The Lord of the Rings. He made several attempts at writing this sequel, but never got very far with it, quite simply because the world of Arda in the Fourth Age didn't make for a good setting for high fantasy writing. Remember that after the end of the Third Age of Middle-Earth, there are no longer any elves, dwarves, orcs, dragons or other fantastic creatures left, each of them either having gone extinct or left for The Undying Lands.
The attempted and abandoned sequel takes place in Gondor, approximately 100 years after the fall of Sauron and the destruction of the One Ring. The idea behind the sequel was to bring out the darkness in the hearts of humans, showing that while Sauron was dead and Morgoth banished from the world, evil could still find ways to take hold. Unfortunately, Tolkien was never satisfied with it, partially because the evil of humanity in Middle-Earth was already well-chronicled in The Fall of Numenor (part of The Silmarillion). He remarked:
"I did begin a story placed about 100 years after the downfall of Sauron, but it proved both sinister and depressing. Since we are dealing with Men it is inevitable that we should be concerned with the most regrettable feature of their nature: their quick satiety with good. So that the people of Gondor in times of peace and justice and prosperity would become discontented and restless - while the dynasts descended from Aragorn would become just kings and governors - like Denethor or worse. I found that even so there was an outcrop of revolutionary plots, about a centre of secret Satanistic religion; while Gondorian boys were playing at being Orcs and going around doing damage. I could have written a 'thriller' about the plot and its discovery and overthrow - but it would be just that. Not worth doing."
The unfinished story was published by J.R.R. Tolkien's son, Christopher Tolkien, in his book Peoples of Middle-Earth.
Personally I can certainly see how it would be hard to do The Lord of the Rings and the Silmarillion justice with a sequel, especially one that cannot take place in a high fantasy setting. But more to the point, Tolkien deciding to abandon the sequel sort of confirms me in what has always been my opinion about the ending of the Lord of the Rings: It's depressing. Well, yes, good triumphs and evil is defeated and all that, but the world of Middle-Earth turns a significant deal more boring. It changes from a fantastic setting to a mundane one. While the humans of Middle-Earth certainly played an important role in giving that world its unique personality (the "land viking"-like culture of Rohan's eorlings always fascinated me, for instance), it was the dwarves, orcs, hobbits, elves, dragons, beornings, Tom Bombadils and Maiar-eagles that set it apart from the world we can see outside our windows. A decent sequel to the Lord of the Rings set in a world without the fantastic would be nigh-on impossible.