Perhaps demand for alimony brings outcry (7)
I believe the answer is:
exclaim
'outcry' is the definition.
(I know that outcry can be written as exclaim)
'perhaps demand for alimony' is the wordplay.
I cannot quite see how this works, but
'demand' could be 'claim' (claim is a kind of demand) and 'claim' is found within the answer.
The remaining letters 'ex' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'brings' is the link.
Can you help me to learn more?
(Other definitions for exclaim that I've seen before include "Cry out suddenly, as from pain or surprise" , "Call" , "Express surprise" , "Cry out (in shock, etc)" , "speak out boldly" .)