Close shaven, cutting head (7)
I believe the answer is:
airless
'close' is the definition.
(synonyms)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for airless that I've seen before include "Unventilated" , "Very stuffy" , "Stifling" , "Not ventilated" , "Still" .)