This colony was the site of negotiations between the Federation and the Klingon Empire in 2289 whose aim was an end to the decades-old cold war between the two. The Federation was represented in the negotiations by Curzon Dax, while the Klingons were represented by Kang, along with Koloth.
Though ultimately unsuccessful, the negotiations did provide a sort of detente that created the conditions that allowed for more serious negotiations several years later when the Klingon moon of Praxis exploded, threatening the survival of their homeworld.
Background information Edit
This colony was only mentioned in dialogue.
According to the script, Korvat was pronounced as "KOR-vat". 
The affiliation of Korvat colony has never been clearly stated on screen, although the Star Trek: The Lost Era and Star Trek: Destiny novels ascribe it to the Klingon Empire. StarTrek.com identified it as a Klingon colony and stated that it was "not clear whether the proper name refers to a planet, star or other such landmark." In the Star Trek: Discovery episode "Magic to Make the Sanest Man Go Mad", the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery, which located Korvat in the Beta Quadrant, depicted this star as being Klingon-held.
According to Star Trek Star Charts (p. 62) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), in the late 24th century, Korvat's system was a Federation system.
The novel The Sorrows of Empire depicts the Korvat negotiations taking place between the Klingons and the Terran Empire in the mirror universe. The mirror counterparts of Curzon Dax and Kang were present, as were those of Gorkon and General Chang.