Criminals greeting first offender in back street (7)
I believe the answer is:
thieves
'criminals' is the definition.
(thief is a kind of criminal)
'greeting first offender in back street' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'first offender' becomes 'eve' (I can't explain this - if you can you should believe this answer much more).
'in' is an insertion indicator.
'back' says the letters should be written backwards.
'street' becomes 'st' (abbreviation).
'st' backwards is 'ts'.
'hi'+'eve'='hieve'
'hieve' inserted inside 'ts' is 'THIEVES'.
Can you help me to learn more?
(Other definitions for thieves that I've seen before include "Light-fingered people" , "People who steal" , "Unit of length" , "They pinch" , "They may be thick" .)