The Temporal Displacement Office (TDO) was an agency situated within the United Federation of Planets which dealt with matters relating to individuals that were displaced from one time period to the current one. By 2376, there was a crew member on Captain Elizabeth Shelby's ship who was displaced by a device resembling an Iconian gateway with her report being filed to the TDO. (TNG - Gateways novel: Doors Into Chaos)

Presumably, this agency was a branch of the Department of Temporal Investigations.