Caught after Sid's criminal record (4)
I believe the answer is:
disc
'record' is the definition.
('disc' can be a synonym of 'record')
'caught after sid's criminal' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'after' means one lot of letters go next to another.
'criminal' indicates anagramming the letters.
'sid' anagrammed gives 'dis'.
'c' after 'dis' is 'DISC'.
(Other definitions for disc that I've seen before include "Forty-five" , "Body without limbs" , "Sound recording" , "Circular flat structure in the spine" , "Old record" .)