Undertaking demand after short time (4)
I believe the answer is:
task
'undertaking' is the definition.
('task' can be a synonym of 'undertaking')
'demand after short time' is the wordplay.
'demand' becomes 'ask' ('ask' can be a synonym of 'demand').
'after' is a charade indicator (letters next to each other).
'short time' becomes 't' (abbreviation for time).
'ask' put after 't' is 'TASK'.
(Other definitions for task that I've seen before include "Piece of work to be done" , "Arduous bit of work" , "exercise" , "Give mission" , "commission" .)