Indifference shown by a nincompoop turning head (9)
I believe the answer is:
aloofness
'indifference' is the definition.
(aloofness is a kind of indifference)
'a nincompoop turning head' is the wordplay.
'nincompoop' becomes 'fool' (I've seen this before).
'turning' is a reversal indicator.
'head' becomes 'ness' (both can mean a promontory).
'fool' written backwards gives 'loof'.
'a'+'loof'+'ness'='ALOOFNESS'
'shown by' acts as a link.
(Other definitions for aloofness that I've seen before include "Haughty nature" , "Indifference by personal withdrawal" , "Indifference, reserve" , "Detachment" , "Cool and distant manner" .)