Kling was a location within the Klingon Empire. Its location in the Alpha Quadrant of the Milky Way Galaxy was depicted on a Federation star chart in 2293. (Star Trek VI: The Undiscovered Country, production art)
According to The Worlds of the Federation (pg. 45), Kling or Klinzhai were names for the Klingon Homeworld. According to Star Trek: Star Charts (pg. 55), Kling was an alternate name for Qo'noS. According to the Star Trek Encyclopedia, Kling was only a "A district or city on the Klingon Homeworld."
According to the Star Trek Encyclopedia, at the time "Heart of Glory" was written, Kling was in fact intended to be the name of the Klingon Homeworld. Once the episode was filmed though, it was realized that the name sounded pretty silly, so later scripts simply referred to "the Homeworld." The next time the Homeworld was given a name was in Star Trek VI: The Undiscovered Country, when it was called "Kronos". The spelling "Qo'noS" was subsequently devised by Marc Okrand, in order to conform to his previously developed rules of Klingon orthography.
The short story A Warrior's Path in New Worlds, New Civilizations, references Kling as a city on Qo'noS.