Just for the record, a police inspector's cool head (4)
I believe the answer is:
disc
'just for the record a police' is the definition.
I can't tell whether this definition defines the answer.
'inspector's cool head' is the wordplay.
'inspector's' becomes 'di's' (abbreviation for Detective Inspector).
'head' says to take the initial letters.
The first letter of 'cool' is 'c'.
'dis'+'c'='DISC'
Can you help me to learn more?
(Other definitions for disc that I've seen before include "Old record" , "CD perhaps" , "Compact ---; slipped ---" , "Flat thin round object" , "put on by jockey?" .)