A holdover is something that has stuck around for a long time. A law that forbids women from wearing patent leather shoes in public is a holdover from a very different era.
The noun holdover comes up often in politics. A member of a former president's cabinet who keeps her job even after a new president is elected may be referred to as a holdover from the previous administration. A gym teacher's habit of barking out instructions to his elementary school students might be a holdover from his army days.