Being unethical, chary about publicity (5)
I believe the answer is:
shady
'being unethical' is the definition.
(thesaurus)
'chary about publicity' is the wordplay.
'chary' becomes 'shy' (I've seen this before).
'about' means one lot of letters goes inside another.
'publicity' becomes 'ad' (short for advert).
'shy' enclosing 'ad' is 'SHADY'.
(Other definitions for shady that I've seen before include "Fishy; unlit" , "underhand" , "Disreputable -- out of the sun" , "Suspicious, fishy" , "Disreputable - umbrageous" .)