Plot outline

While the USS Enterprise escorts two robot cargo ships carrying quintotriticale, a new seed grain, to famine stricken Sherman's Planet, it encounters a Klingon

Klingon

Klingons are a fictional warrior race in the Star Trek universe.Klingons are recurring villains in the 1960s television show Star Trek: The Original Series, and have appeared in all five spin-off series and eight feature films...

 battlecruiser pursuing a Federation scout ship. When the Enterprise rescues the pilot, the Klingons attack with a new energy weapon and demand that the pilot be handed over to them.
The pilot turns out to be Cyrano Jones, an intergalactic trader well known to Kirk and crew from "The Trouble With Tribbles". The Klingons desperately want Jones for introducing the tribble

Tribble

Tribbles are fictional asexual animals in the Star Trek universe who first appeared in the episode titled "The Trouble With Tribbles". They are depicted as small, soft, and gentle, and as producing a soothing purring sound...

 to Klingon planets where it has become a major pest, and for stealing a glommer, an animal the Klingons were breeding to prey on the tribble.
Kirk expresses sympathy for the Klingons' plight but refuses to hand over Jones, a Federation citizen.
Jones is now selling tribbles genetically engineered

Genetic engineering

Genetic engineering, also called genetic modification, is the direct human manipulation of an organism's genome using modern DNA technology. It involves the introduction of foreign DNA or synthetic genes into the organism of interest...

to omit their ordinarily unrestrained multiplicative proclivities. Dr. McCoy discovers that although Jones' "new" tribbles don't reproduce, they still have ravenous appetites. Instead of reproducing, they now grow hugely fat.

Kirk and Spock manage to counter the Klingon weapon. Now at a disadvantage, the Klingons offer to settle for just the glommer. Kirk agrees and returns it—along with several well-fed (and huge) tribbles that scare it away. McCoy injects the remaining tribbles on the Enterprise with a serum to slow down their metabolic rate. They are finally "safe".