The story is centered around Israelis in space, one of whom, the main character is an inspector general sent to solve a problem.
Specifically, the book you're remembering is "Not For Glory" (on Goodreads) by Joel Rosenberg. Tetsuo Hanavi is the protagonist of this book, and holds the (mostly ceremonial) rank of Inspector General. He isn't the real IG; he admits to the reader that his chief subordinate does all of that work. Being IG gives him a cover story to move freely around for his real job as assassin/trouble-shooter.
The main plot of the novel deals with finding and retrieving his missing uncle Bar-El who has sent a cryptic message "The Freiheimers are riveting their tanks" on the eve of negotiations with said Freiheimers for a mercenary contract. In my memory the book is very episodic; a section introduces the readers to Metzada and Tetsuo's family, a section involves extracting Bar-El with the help of some retired relatives, a section involves a neat trick that Bar-El dreams up to get around tech restrictions on a low-tech world...
Goodreads says that this is a 4-book series, but really only this book deals with Tetsuo. "Ties of Blood and Silver" and "Emile and the Dutchman" don't really deal with the Metzadan mercenaries at all, and while Tetsuo appears in "Hero," the main character is Tetsuo's nephew Avi.
Finally found it: The Matzadan mercenary corps. 4 books.