Prove that south is the way (4)
I believe the answer is:
show
'prove' is the definition.
('show' can be a synonym of 'prove')
'south is the way' is the wordplay.
'south' becomes 's' ('S' can be a synonym of 'south').
'is the way' becomes 'how'.
's'+'how'='SHOW'
'that' is the link.
(Other definitions for show that I've seen before include "Expose" , "Screen" , "Performance" , "Demonstrate - parade" , "Prove; exhibit" .)