The DTS is probably best known for its appearance in the traditional New Cycle broadcast, when the Prime Clock marking Upwarp Standard Time rolls over to .00.00/00.00.00.
The Department for Parachronotic Research and Retrieval is a Delta Sector subset of the DST, dedicated to carefully analyzing and retrieving useful and interesting material from other timelines without destabilizing the present timeline... Parachronic Researchers, or chrononauts, often come back from their leaps elsewhen with interesting items or records to further Up's catalogue of knowledge, but with bits of their own history missing. The serpentaur in charge of the Specialized Collection of Pararchaeological Artifacts, for instance, has lost all memory of and references to zir name; zie is referred to merely as The Archivist.
Sadly, many of their legends have unhappened, as have many of the dramatis personae.
The RL analogue of the DST is presumably the [International Earth Rotation and Reference Systems Service], which issues "leap seconds" to keep the various flavours of [Universal Time] in order.
Perhaps the DTS was the creation of a [Sandford Fleming] type character who established it after having a run-in with a time instability himself...