Deteriorates after hospital department charges (8)
I believe the answer is:
entrusts
'charges' is the definition.
(as in charging someone with a task)
'deteriorates after hospital department' is the wordplay.
'deteriorates' becomes 'rusts' (I've seen this in another clue).
'after' means one lot of letters go next to another.
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'rusts' after 'ent' is 'ENTRUSTS'.
(Other definitions for entrusts that I've seen before include "Places in care, so set about runts" , "Puts into the care or protection of" , "Places in a person's safe care" , "Willingly gives responsibility to" , "Commits confidently to another." .)