Dominant state has come down after unrest in Suez? (8)
I believe the answer is:
suzerain
'dominant state' is the definition.
(a suzerain is a state controlling another)
'come down after unrest in suez?' is the wordplay.
'come down' becomes 'rain' (raining is a kind of coming down).
'after' says to put letters next to each other.
'unrest in' indicates anagramming the letters (an unsettled ordering of the letters).
'suez' with letters rearranged gives 'suze'.
'rain' put after 'suze' is 'SUZERAIN'.
'has' is the link.
(Other definitions for suzerain that I've seen before include "Lord" , "Feudal overlord" , "Supreme ruler; azure sin (anag.)" .)