The USS Wellington experienced a disastrous away mission at Garon II in the mid-2360s. During the mission, Lieutenant Ro Laren disobeyed direct orders, resulting in the deaths of eight of her fellow officers. Ro was subsequently court martialed for her actions. She was demoted to the rank of ensign and sentenced to imprisonment in the stockade on Jaros II. (TNG: "Ensign Ro", "Conundrum")
During Ro's memorial service later that year, Jean-Luc Picard stated that if she hadn't lost her rank as a result of the incident, he felt she would have been a lieutenant commander by late 2368. (TNG: "The Next Phase")
Background information Edit
This planet was only mentioned in dialogue.
"GAH-run" was the pronunciation for this planet's name from the script pronunciation guide for "Ensign Ro". 
In the remastered "Conundrum", the incident on Garon II was mentioned as a note in Ensign Ro Laren's personnel file from the Crew Manifest Database.
In "The Next Phase", Picard noted that the incident resulting in Ro's demotion took place on "Garon IV" rather than "Garon II."