Place it at the very end of a timed segment, after the countdown and before the reaction, so it marks the close. Lead into it with Dun Dun Dun, then follow it with Classic Error Sound when the player misses the deadline.
About this sound
This is a very short parental-controls alert, lasting under a second, built around a voice announcing that time is up. The clipped delivery feels abrupt and final, like a firm cutoff rather than a gentle warning, which makes it funny when it lands on someone else and tense when it lands on you. It comes from the Windows parental-controls time-limit alert.