The Loonkerian outpost was an outpost located on the planet Klendth.

Sometime prior to 2285, a piece of technology, known as the universal atmospheric element compensator was made on the Loonkerian outpost.

Spock was asked about this technology in his memory test on Vulcan following his "rebirth" on Genesis Planet several months earlier. (Star Trek IV: The Voyage Home)

This outpost was only mentioned in dialogue.
According to the movie's closed captioning, the spelling for this outpost was "Locnaerian".