A station manager was someone who oversaw a space station.
In 2268, Mister Lurry was the station manager of Deep Space Station K-7. When Koloth requested permission to take shore leave there, Captain Kirk told him that it was Lurry's decision, not his, but Lurry took Kirk aside and said he didn't have the authority to refuse the Klingon's request. (TOS: "The Trouble with Tribbles"). While time traveling with several other crew members from Deep Space 9, Kira Nerys observed Koloth and Korax's beam out from the Klingon ship. (DS9: "Trials and Tribble-ations")