Hold-up man in downbeat LA suburb (5)
I believe the answer is:
atlas
'hold-up man' is the definition.
(Greek mythology - he held up the world)
'in downbeat la suburb' is the wordplay.
'in' indicates a hidden word.
'ATLAS' is hidden within 'downbeat la suburb'.
(Other definitions for atlas that I've seen before include "Titan who bore the sky on his shoulders" , "Holder of world" , "Sort of book" , "African mountain range" , "The first cervical vertebra" .)