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 definition defines the answer.
'cool head on operations' is the wordplay.
'head' says to take the initial letters.
'on' is a charade indicator (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.)" .)