Duke is heading for criminal record (4)
I believe the answer is:
disc
'record' is the definition.
(eg a CD, compact disc)
'duke is heading for criminal' is the wordplay.
'duke' becomes 'd' (abbreviation).
'heading for' suggests taking the first letters.
The initial letter of 'criminal' is 'c'.
'd'+'is'+'c'='DISC'
(Other definitions for disc that I've seen before include "Circular flat structure in the spine" , "Forty-five" , "Body without limbs" , "Sound recording" , "Layer of cartilege between vertebrae" .)