A look of being indifferent (5)
I believe the answer is:
aloof
'indifferent' is the definition.
(thesaurus)
'a look of' is the wordplay.
'look' becomes 'lo'.
'a'+'lo'+'of'='ALOOF'
'being' acts as a link.
(Other definitions for aloof that I've seen before include "Distant or stuck-up" , "Withdrawn, supercilious" , "Displaying supercilious reserve" , "Haughty and distant like a fool" , "apart from all else" .)