Head-hunter ignores Alabama for a bit (4)
I believe the answer is:
some
'for a bit' is the definition.
(I've seen this in another clue)
'head-hunter ignores alabama' is the wordplay.
'head-hunter' becomes 'Salome' (Salome asked for the head of John the Baptist).
'ignores' is a deletion indicator.
'alabama' becomes 'al'.
'salome' with 'al' taken away is 'SOME'.
(Other definitions for some that I've seen before include "Part" , "Hard work" , "certain" , "Undefined number" , "An undetermined number" .)