Make one's way to the West End (4)
I believe the answer is:
wend
'make one's way' is the definition.
(I've seen this before)
'the west end' is the wordplay.
'the west' becomes 'W' (abbreviation).
'w'+'end'='WEND'
'to' is the link.
(Other definitions for wend that I've seen before include "... one's way, go on a journey" , "Slowly go" , "Slav" , "Make (ones way)" , "Travel" .)