The Temporal Displacement Division (or Temporal Displacement Office; TDO) was a Federation agency, a section within the Federation Department of Temporal Investigations charged with dealing with matters relating to individuals displaced from one time period to the current one.

By the year 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)

In 2376, DTI Special Agent Marion Dulmur was a supervisor in the Temporal Displacement Division, with Stewart Peart as one of the agents serving underneath him. (NF short story: "The Road to Edos")

Starfleet Admiral Gulliver was also attached to the Temporal Displacement Division, in a role where he dealt specifically with displaced Starfleet officers. (NF - Gateways novel: Cold Wars)

After being transported to 2286, the 20th century marine biologist Gillian Taylor became the TDD's inaugural patient.

In 2368, Clare Raymond, a 20th century homemaker who had spent 370 years in cryonic stasis before being discovered by the crew of the USS Enterprise-D in 2364, began working as a counselor for the TDD. She retained that position until at least 2382. (DTI novel: Watching the Clock)

In Cold Wars, Gulliver states he represents "the Starfleet Department for Temporally Displaced Officers," though the relevant scene takes place within the (presumably civilian) Department of Temporal Investigations, and his function appears largely the same as that of Dulmur and Peart in "The Road to Edos." It is unclear whether this is an alternate name for the same organization, or a discrete organization within or associated with the DTI.
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