Actually JRRT started a new story which took place in the 4th age, under Eldarion's reign, but soon abandoned it.
I'm sure Christopher Tolkien would never start a new book if his father wouldn't have asked him to before his death. JRRT only asked Christopher to assemble the Silmarillion, not a sequel to LOTR.
So, such a book won't come in a million aeons. It's like asking for a sequel to the Bible.
Heck, aren't all those cheesy post-LOTR fanfiction stories enough?
PJ is already making a new LOTR flick, with a strange title : 'Return of the King Kong'. I wonder what that will be about. Probably about the monkey business in Middle-Earth after Elessar became king.
Give up the Halfring, she-elf...