The Gripping Hand revolves primarily around two minor characters of the first book, Captain Sir Kevin Renner (ISN, Reserve) and His Excellency Horace Bury, Imperial Trader Magnate. It also resolves many of the conflicts and tension remaining from the preceding novel, but much of the plot cannot be understood without reading The Mote in God's Eye. A crucial plot element of the book is the idiom "on the gripping hand", a three-armed variation of the idiom "on the other hand" similar in meaning to "on the third hand", but with the added sense that the third-mentioned consideration is the most important one. The saying is native to the alien Moties, who have three arms, one of which is stronger but possesses less finesse.
At the end of The Mote in God's Eye, Renner and Bury are secretly enlisted into Imperial Naval Intelligence. They spend the next twenty-five years investigating revolutions against the Empire so that the Imperial Navy can concentrate on blockading the Moties from entering into human space. While investigating economic abnormalities on the Mormon planet Maxroy's Purchase, Renner and Bury encounter widespread use of the phrase "on the gripping hand". While the source of the phrase turns out to be innocuous enough — the Governor picked up the expression as an Able Spacer on INSS MacArthur on the expedition to Mote Prime — the memories dredged up by the incident are too much for Bury. Driven by nightmares and a deep-seated fear for humanity's safety, Bury must confirm that the Empire is safe from the Moties.
Renner and Bury travel first to Sparta, the Imperial? capital planet, to obtain permission to inspect the blockade. Along the way, they discover widespread interest in a second expedition to the Mote, as well as disturbing evidence that the blockade may soon fail.