Old Bill, showing a cool head on operations (4)
I believe the answer is:
cops
'old bill showing a' is the definition.
I can't judge whether this defines the answer.
'cool head on operations' is the wordplay.
'head' indicates taking the first letters.
'on' says to put letters next to each other.
'operations' becomes 'ops' (abbreviation).
The initial letter of 'cool' is 'c'.
'c'+'ops'='COPS'
Can you help me to learn more?
(Other definitions for cops that I've seen before include "Familiar American policemen" , "Panda owners" , "Police (slang)" , "The police (sl.)" .)