Domination of the Spithead route (4)
I believe the answer is:
sway
'domination' is the definition.
(thesaurus)
'spithead route' is the wordplay.
'spithead' becomes 's' (head letter of 'spit').
'route' becomes 'way' (way is a kind of route).
's'+'way'='SWAY'
'of the' is the link.
(Other definitions for sway that I've seen before include "Control" , "Rock to and fro" , "Power - rock" , "Move gently" , "Influence; dominance" .)