Learn English – it called when you are sent by the organization you work for to do a one day task in another city

If any kind of digital clock or calendar is in the picture, then rollover can describe this.

It needs a little context to make it clear: e.g. something like “Nominations open Saturday February 21, at the rollover” may not be understood by all readers, but “Nominations open at midnight, on the rollover from Fri 20 to Sat 21” should be well understood, as should “Nominations open Friday night, at the rollover from 11:59 to 12:00”.

Are you perhaps referring to the word "Tribe"?

A tribe is normally an organization that consists of many clans.

For example, The barbarians of Icewind Dale were all a large group that lived in the harsh wastes in the North of The Forgotten Realms. Each had their own designation, Such as Tribe of the Elk, Tribe of the Bear, Tribe of the Tiger, etc. And each Tribe had clans that while still belonging to those Tribes, were separate entities.

Those Barbarians were still members of the Larger tribe, they just lived in their own clan and took orders from the leader of their tribe.