Initially smart approach to gain influence (4)
I believe the answer is:
sway
'influence' is the definition.
(I know that sway is a more specific form of the action influence)
'initially smart approach' is the wordplay.
'initially' says to take the initial letters.
'approach' becomes 'way' (a way of doing something).
The initial letter of 'smart' is 's'.
's'+'way'='SWAY'
'to gain' is the link.
(Other definitions for sway that I've seen before include "Pitch sideways" , "Influence; dominance" , "Bend; influence" , "Control" , "Move back and forth" .)