Underling attached to party in power (8)
I believe the answer is:
dominion
'power' is the definition.
(thesaurus)
'underling attached to party' is the wordplay.
'underling' becomes 'minion' (I've seen this before).
'attached to' says to put letters next to each other.
'party' becomes 'do' (do is a kind of party).
'minion' put after 'do' is 'DOMINION'.
'in' is the link.
(Other definitions for dominion that I've seen before include "Sovereignty, control" , "power" , "Government" , "Territorial possession controlled by a ruling state" , "Authority to rule over and control people" .)