Married woman initially detecting crime (5)
I believe the answer is:
fraud
'crime' is the definition.
(fraud is a crime)
'married woman initially detecting' is the wordplay.
'married woman' becomes 'frau' (title for a married woman in German).
'initially' says to take the initial letters.
The first letter of 'detecting' is 'd'.
'frau'+'d'='FRAUD'
(Other definitions for fraud that I've seen before include "Scam" , "Imposter - deceit" , "Criminal deception" , "act of deception" , "Duplicity" .)