Later that year, this cluster's location was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. (TNG: "The Vengeance Factor"; DIS: "Magic to Make the Sanest Man Go Mad")
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 Star Trek: Star Charts (pp. 61, 62) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), 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.
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).