short notice, on
Also, at short notice. With little advance warning or time to prepare, as in They told us to be ready to move out on short notice. The noun notice here is used in the sense of “information” or “intelligence.” [Late 1700s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.