Lacking common sense, boss employing Greek character (6)
I believe the answer is:
stupid
'lacking common sense' is the definition.
(I've seen this before)
'boss employing greek character' is the wordplay.
'boss' becomes 'stud' ('stud' can be a synonym of 'boss').
'employing' means one lot of letters goes inside another.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'stud' going around 'pi' is 'STUPID'.
(Other definitions for stupid that I've seen before include "Irresponsible" , "Asinine" , "Dim" , "dope" , "Very silly" .)