(covers information from several alternate timelines)
In that year, the Human Captain Jonathan Archer was put on trial on Narendra III, under the suspicion of conspiring against the Klingon Empire. Archer was sentenced to lifelong exile on Rura Penthe, and his advocate Kolos had to join him for one year. However, Archer was later rescued from Rura Penthe by his crew. (ENT: "Judgment")
In 2344, the outpost was attacked and destroyed by four Romulan warbirds, an assault which was later known as the Battle of Narendra III. The Federation starship USS Enterprise-C responded to the outpost's distress call, but was also lost in the battle. This course of action was considered as an act of honor by the Klingon Empire, which led to the signing of a new peace treaty.
In an alternate timeline, the Enterprise-C disappeared during the battle. The outpost was destroyed, and events led to a renewed conflict between the Federation and the Empire. (TNG: "Yesterday's Enterprise", "Redemption II")
Background information Edit
According to Eric A. Stillwell, this planet was named after Star Trek: The Next Generation writer and science consultant Naren Shankar. (citation needed • edit) "nah-REN-druh" was how the planet's name was phonetically spelled in the script pronunciation guide for "Yesterday's Enterprise". 
Although the planet shown in "Judgment" is never identified as Narendra III on screen (the term "Narendra" is not mentioned there at all), the episode's final draft script referred to it as such.  Also, David A. Goodman, the episode's writer, stated in a podcast that he intended for the settlement/installation shown to refer to the outpost from "Yesterday's Enterprise".
In the final draft script of "Judgment", an overview of an area on Narendra III shown in that installment was described as "A large city on this Klingon outpost, with familiar Klingon-style architecture. In the center of town, a GRAND TRIBUNAL BUILDING which proudly displays the three-pointed Klingon symbol." 
According to Star Trek: Star Charts (p. 64), the Narendra system was located in or near Klingon space, in the Beta Quadrant. This system was a binary star system. The primary was a class K star with a magnitude of +3, which was ten times brighter than Sol. The secondary was a class A star.