The Starfleet office responsible for investigating the conduct of ships and officers, whose representative Dexter Remmick interrogated the Enterprise-D crew about Captain Picard in 2364.
The Inspector General's office is Starfleet's internal watchdog, with authority to examine the records and decisions of any command.
It appears in the Next Generation episode Coming of Age. Admiral Gregory Quinn boards the Enterprise-D with Lieutenant Commander Dexter Remmick of the Inspector General's office and orders a full inquiry without stating the reason. Remmick questions the senior staff in turn about past incidents, antagonising everyone, but has to report that he found nothing wrong beyond a crew devoted to its captain.
Quinn then admits he fears that something is undermining Starfleet and wanted to be certain of Picard, whom he asks to take charge of the Academy. The suspicion is borne out in Conspiracy, where Remmick is the host of the parasites' mother creature.