In the short term: No.
In the long term: We don't know, but possibly not.
To expand on this a little: Peter Jackson had the rights to make films based on the published books The Hobbit and The Lord of the Rings. (The real legal situation is substantially more complicated, but that sums it up.)
The remaining rights to JRR Tolkien's work are held by his son, Christopher Tolkien. He is well known to be extremely protective of his father's literary legacy. For a long time, he has been in conflict with Peter Jackson, New Line, and Warner Brothers over money and the creative direction of the films. This article has some more details, including the following quote from Christopher in relation to the Lord of the Rings films:
They gutted the book, making an action movie for 15-25 year olds. And it seems that The Hobbit will be of the same ilk. Tolkien became...devoured by his popularity and absorbed by the absurdity of the time. The gap widened between the beauty, the seriousness of the work, and what it has become is beyond me. This level of marketing reduces to nothing the aesthetic and philosophical significance of this work.
The chances of Christopher authorising more big-budget films based on his father's work are effectively nil. Similar considerations apply to writing more books. For more than 40 years, Christopher has confined his role to editing and commenting on his father's writing. He is highly unlikely to start writing original material at this point, or allow anyone else to do so.
Christopher is 90 years old (born 1924) and will not be with us forever. After his passing, future decisions about Tolkien's work will be left to his heirs. We do not know what they will decide (and it would be unseemly to speculate too much), but it is at least plausible they will continue the direction followed by Christopher, and refuse to authorise any further adaptation or extension of Tolkien's works.
On 2017-08-31, Christopher Tolkien retired as director of the Tolkien estate. As it turns out, the new controllers of the estate are open to further adaptations of JRR Tolkien's work:
Now that Christopher Tolkien has retired, the “rights frenzy” for his properties can begin, as Tolkien enthusiast Michael Martinez wrote on his blog. Currently, the plans are for an Amazon series set in the world of The Lord of the Rings, which reportedly came after a bidding war between several networks. Given that Tolkien Estate incorporated in 2011 and Christopher Tolkien is no longer holding the reins, it looks to be open season for Tolkien films, shows, theme parks, or pretty much anything else you could imagine.
The Amazon series was confirmed on 2017-11-13.