Police operation tailing short criminal is persistent (7)
I believe the answer is:
lasting
'persistent' is the definition.
(I know that persistent can be written as lasting)
'police operation tailing short criminal' is the wordplay.
'police operation' becomes 'sting' (I've seen this in another clue).
'tailing' says to put letters next to each other (to tail can mean to go after or follow).
'short' means to remove the last letter.
'criminal' becomes 'lag' (slang term for a prisoner).
'lag' with its last letter taken off is 'la'.
'sting' after 'la' is 'LASTING'.
'is' is the link.
(Other definitions for lasting that I've seen before include "there for long while" , "Abiding, durable" , "Long-lived" , "Enduring" , "Permanent" .)