(written from a Production point of view)
A photo of this bookshelf appeared in the Twitter account of Star Trek: Discovery producer Aaron Baiers. The title of this book, and other books on the shelf, were Star Trek: The Original Series episode titles, and were described as "Easter eggs for all Trek lovers". 
However, the shelf as it appeared on screen counted fewer books, and since the titles were not obviously readable, it is unclear which were removed and which remained.
This book's title refers to the episode "The Trouble with Tribbles". In-universe, it might have dealt with tribbles, which had been known to Starfleet, at least since the era of of Star Trek: Enterprise (Dr. Phlox possessed some), and Captain Gabriel Lorca kept one in his ready room aboard the USS Discovery.