Honour independent Greek character (3)
I believe the answer is:
chi
'greek character' is the definition.
(letter from the Greek alphabet)
'honour independent' is the wordplay.
'honour' becomes 'ch' (**).
'independent' becomes 'i'.
'ch'+'i'='CHI'
(Other definitions for chi that I've seen before include "Letter written by European" , "Greek X" , "Chinese life-force" , "The 22nd letter of Greek alphabet" , "T'ai -, martial art" .)