Declare old partner's demand for alimony (7)
I believe the answer is:
exclaim
'declare' is the definition.
(I know that declare is a more specific form of the action exclaim)
'old partner's demand for alimony' is the wordplay.
I cannot really understand how this works, but
'old' could be 'ex' (prefix meaning former or onetime) and 'ex' is present in the answer.
'demand' could be 'claim' (claim is a kind of demand) and 'claim' is located in the answer.
No letters remain.
This explanation may well be incorrect...
(Other definitions for exclaim that I've seen before include "Cry out suddenly, as from pain or surprise" , "Speak suddenly" , "Declare" , "Announce vehemently" , "Shout out" .)