Approaches northeast, not starting far south (5)
I believe the answer is:
nears
'approaches' is the definition.
(I know this)
'northeast not starting far south' is the wordplay.
'northeast' becomes 'NE' (abbreviation).
'not starting' means to remove the first letter.
'south' becomes 'S' (abbreviation).
'far' with its initial letter removed is 'ar'.
'ne'+'ar'+'s'='NEARS'
(Other definitions for nears that I've seen before include "Comes closer" , "Gets closer" , "Bears down" , "Moves towards" , "Becomes closer" .)