Compete with West, see! (4)
I believe the answer is:
view
'see' is the definition.
(I know that see can be written as view)
'compete with west' is the wordplay.
'compete with' becomes 'vie' (to vie with someone is to compete with them).
'west' becomes 'W' (abbreviation).
'vie'+'w'='VIEW'
(Other definitions for view that I've seen before include "Prospect - opinion" , "Outlook" , "Regard" , "'Aspect, panorama (4)'" , "belief" .)