Private soldier, second one of four to go west (8)
I believe the answer is:
squaddie
'private soldier' is the definition.
(I've seen this before)
'second one of four to go west' is the wordplay.
'second' becomes 's' (common abbreviation).
'one of four' becomes 'quad' (short for quadruplet, one of four children).
'to go west' becomes 'die' (to go west can informally mean to die).
's'+'quad'+'die'='SQUADDIE'
(Other definitions for squaddie that I've seen before include "Nickname for a private soldier in the Army" , "Private Tommy Atkins?" , "Private soldier (informal)" , "Ordinary soldier (informal)" , "Private soldier (colloq.)" .)