Detective's heading for criminal record (4)
I believe the answer is:
disc
'record' is the definition.
('disc' can be a synonym of 'record')
'detective's heading for criminal' is the wordplay.
'detective's' becomes 'dis' (Detective Inspector).
'heading for' says to take the initial letters.
The initial letter of 'criminal' is 'c'.
'dis'+'c'='DISC'
(Other definitions for disc that I've seen before include "Thin flat circular object" , "One of 33, 45 or 78?" , "Flat round plate" , "Record, CD" , "Layer of cartilege between vertebrae" .)