Conflict with desperate sweetheart about droop (8)
I believe the answer is:
disagree
'conflict with' is the definition.
(thesaurus)
'desperate sweetheart about droop' is the wordplay.
'desperate' becomes 'dire' (I've seen this before).
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'about' means one lot of letters goes inside another.
'droop' becomes 'sag' ('sag' can be a synonym of 'droop').
'dire'+'e'='diree'
'diree' placed around 'sag' is 'DISAGREE'.
(Other definitions for disagree that I've seen before include "Be at variance" , "Beg to differ" , "Dire ages (anag.)" , "Quarrel" , "Differ, argue" .)