Policeman's way of cutting hair close (5)
I believe the answer is:
bobby
'policeman's' is the definition.
(bobby is a kind of policeman)
'way of cutting hair close' is the wordplay.
'way of cutting hair' becomes 'bob' (to cut into a bob).
'close' becomes 'by' (I've seen this in other clues).
'bob'+'by'='BOBBY'
(Other definitions for bobby that I've seen before include "Peeler" , "-- Moore; -- Charlton (footballers)" , "Policeman (sl.)" , "Policeman (colloq.)" , "Cop (slang)" .)