Caring terribly about hospital's discomfiture (7)
I believe the answer is:
chagrin
'discomfiture' is the definition.
(thesaurus)
'caring terribly about hospital's' is the wordplay.
'terribly' indicates anagramming the letters.
'about' means one lot of letters goes inside another.
'hospital' becomes 'h'.
'caring' anagrammed gives 'cagrin'.
'cagrin' enclosing 'h' is 'CHAGRIN'.
(Other definitions for chagrin that I've seen before include "Embarrassment - rich nag (anag)" , "Shame at having failed" , "Arching with annoyed disappointment" , "Disappointment, exasperation" , "irritation?" .)