A specified first offender covered for criminals (7)
I believe the answer is:
thieves
'for criminals' is the definition.
(thief is a kind of criminal)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for thieves that I've seen before include "Having a kitchen" , "They may be thick" , "They pinch" , "Stealers" , "Crooks" .)