Pesters Republican surrounded by emblems (7)
I believe the answer is:
badgers
'pesters' is the definition.
('badger' can be a synonym of 'pester')
'republican surrounded by emblems' is the wordplay.
'republican' becomes 'R' (abbreviation in US politics).
'surrounded by' is an insertion indicator.
'emblems' becomes 'badges' (badge is a kind of emblem).
'r' put within 'badges' is 'BADGERS'.
(Other definitions for badgers that I've seen before include "Burrowing mammals with strong claws" , "Pesters like burrowing animals" , "Bullies" , "Pesters; black and white nocturnal animals" .)