It's left controlling local political system (8)
I believe the answer is:
republic
'political system' is the definition.
(I know that republic is a type of political regime)
'it's left controlling local' is the wordplay.
'it's left' becomes 'relic' (I am not sure about this - if you are sure you should believe this answer much more).
'controlling' is an insertion indicator.
'local' becomes 'pub' (one's local pub).
'relic' going around 'pub' is 'REPUBLIC'.
Can you help me to learn more?
(Other definitions for republic that I've seen before include "Non-monarchical state" , "State in which the people hold the power" , "Strange pub relic of a political system" , "Nation in which the head of state is elected" , "The political system is an epic blur" .)