The Federation had charted, but not explored, several M-class planets in this cluster by 2366, including Gamma Hromi II. That year, the USS Enterprise-D entered the Hromi Cluster to locate a Gatherer outpost. (TNG: "The Vengeance Factor")
Background information Edit
According to the Star Trek: Star Charts, the Hromi Cluster was located in the Beta Quadrant. In 2293, the USS Enterprise either passed through the outer rim of this cluster, or passed near to the cluster, when the starship was on a diplomatic mission to Qo'noS. (pp. 61 & 62).
In the backstory to Star Trek Online, in 2404 the Klingon Empire's Chancellor J'mpok (β) invoked ancient Klingon claims to the Hromi Cluster and demanded that all Federation citizens evacuate within three months. The Federation refused, and in 2405 the region became the first battleground of the Federation-Klingon War of 2405-2410 (β).