1
general::
The period of time allowed for something is ended, as in Turn in your papers, students; time is up. This idiom uses up in the sense of "completed" or "expired," a usage dating from about 1400.
American Heritage Idioms
2
general::
Phrase(s): Time is up.
Fig. The allotted time has run out. • You must stop now. Your time is up. • Time’s up! Turn in your tests whether you’re finished or not.
McGrawhill's American Idioms And Phrasal Verbs