Gangster pursues demure chief (6)
I believe the answer is:
primal
'chief' is the definition.
(I've seen this in another clue)
'gangster pursues demure' is the wordplay.
'gangster' becomes 'al' (Al Capone).
'pursues' is a charade indicator (letters next to each other).
'demure' becomes 'prim' (I've seen this before).
'al' put after 'prim' is 'PRIMAL'.
(Other definitions for primal that I've seen before include "Original, fundamental" , "Sort of scream" , "Most important (scream therapy?)" , "Of an early stage of development" , "Existing from the beginning, basic" .)