Some clinics sent penicillin back, showing incompetence (9)
I believe the answer is:
ineptness
'incompetence' is the definition.
(ineptness is a kind of incompetence)
'some clinics sent penicillin back' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'back' says the letters should be written backwards.
'ssentpeni' can be found hidden inside 'clinics sent penicillin'.
'ssentpeni' backwards is 'INEPTNESS'.
'showing' acts as a link.
(Other definitions for ineptness that I've seen before include "Clumsiness, lack of skill" , "Lack of suitability" , "Awkwardness, clumsiness" .)