Anger after hospital department's full (6)
I believe the answer is:
entire
'full' is the definition.
('entire' can be a synonym of 'full')
'anger after hospital department's' is the wordplay.
'anger' becomes 'ire' ('ire' can be a synonym of 'anger').
'after' means one lot of letters go next to another.
'hospital department' becomes 'ent'.
'ire' after 'ent' is 'ENTIRE'.
(Other definitions for entire that I've seen before include "Utter" , "everything" , "outright" , "With no part left out" , "Whole and complete" .)