Trouble after hospital department's demand (6)
I believe the answer is:
entail
'demand' is the definition.
(I've seen this in another clue)
'trouble after hospital department's' is the wordplay.
'trouble' becomes 'ail' (synonyms).
'after' is a charade indicator (letters next to each other).
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'ail' after 'ent' is 'ENTAIL'.
(Other definitions for entail that I've seen before include "Cut" , "Involve or make necessary" , "Call for" , "settlement of estate" , "Restriction on inheritance" .)