Notice tiny country in which Republican is to run (12)
I believe the answer is:
administrate
'is to run' is the definition.
(I've seen this before)
'notice tiny country in which republican' is the wordplay.
'notice' becomes 'ad' (short for advert).
'tiny' becomes 'mini'.
'country' becomes 'state' (synonyms).
'in which' is an insertion indicator.
'republican' becomes 'R' (abbreviation in US politics).
'state' going around 'r' is 'strate'.
'ad'+'mini'+'strate'='ADMINISTRATE'
(Other definitions for administrate that I've seen before include "Manage - it's marinated (anag)" , "Organise (business)" , "direct" , "Run" .)