Sign about half the population wants leader ousted (4)
I believe the answer is:
omen
'sign' is the definition.
(I know that omen is a type of sign)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for omen that I've seen before include "Warning - sign" , "Augur" , "Portent of things to come" , "Foreshadow" , "Harbinger, augury" .)