Girl starts to suspect criminal record (4)
I believe the answer is:
disc
'record' is the definition.
('disc' can be a synonym of 'record')
'girl starts to suspect criminal' is the wordplay.
'girl' becomes 'di' (**).
'starts to' suggests taking the first letters.
The initial letters of 'suspect criminal' is 'sc'.
'di'+'sc'='DISC'
(Other definitions for disc that I've seen before include "In Olympic event" , "Thin flat circular object" , "Forty-five" , "Thin circular plate, as in CD" , "Capital of India" .)