"Very well, Potter, I will take your word for it this time, but be warned: the might of the Ministry stands behind me. All channels of communication in and out of this school are being monitored. A Floo Network Regulator is keeping watch over every fire in Hogwarts - except my own, of course. My Inquisitorial Squad is opening and reading all owl post entering and leaving the castle. And Mr Filch is observing all secret passages in and out of the castle."
—Dolores Umbridge informs Harry Potter of how secure Hogwarts is under her rule[src]

A Floo Network Regulator was a Ministry of Magic employee tasked with policing fireplaces suspected of being used for illegal activity. They were presumably employees of either the Floo Network Authority or the Floo Regulation Panel.

During the 1995-1996 school year, Dolores Umbridge tasked the Floo Network Regulators with monitoring every fireplace at Hogwarts Castle, with the exception of the one in her office. Due to this monitoring, Harry Potter was forced to break into Umbridge's office to ascertain whether Sirius Black had really been kidnapped by Death Eaters and taken to the Hall of Prophecy, as he had seen in a vision caused by his connection to Voldemort.

Known Regulators