Greek character, doctor, lacking any feeling (4)
I believe the answer is:
numb
'lacking any feeling' is the definition.
(numb means lacking feeling)
'greek character doctor' is the wordplay.
'greek character' becomes 'nu' (Greek letter).
'doctor' becomes 'MB' (Bachelor of Medicine, Medicinae Baccalaureus).
'nu'+'mb'='NUMB'
(Other definitions for numb that I've seen before include "Deaden" , "Feeling nothing" , "Insensitive" , "Unable to feel or think" , "Anaesthetised, unfeeling" .)