Greatly agitated about hospital's inertia (8)
I believe the answer is:
lethargy
'inertia' is the definition.
(I've seen this before)
'greatly agitated about hospital's' is the wordplay.
'agitated' indicates anagramming the letters.
'about' means one lot of letters goes inside another.
'hospital' becomes 'h'.
'greatly' is an anagram of 'letargy'.
'letargy' going around 'h' is 'LETHARGY'.
(Other definitions for lethargy that I've seen before include "Torpor" , "'Lassitude, langour (8)'" , "Being sluggish" , "Lack of energy and enthusiasm" , "state of apathy" .)