Aloofness shown in public, in essence (7)
I believe the answer is:
iciness
'aloofness' is the definition.
'shown in public in essence' is the wordplay.
'shown in' says the answer is hidden in the clue.
'ICINESS' is hidden in the letters of 'public in essence'.
(Other definitions for iciness that I've seen before include "Extreme cold" , "Extreme chill" , "Chill; reserve" , "Frozen state of" , "Frostiness" .)