Oily crooked politician entering a state capital (7)
I believe the answer is:
olympia
'state capital' is the definition.
(Olympia is an example)
'oily crooked politician entering a' is the wordplay.
'crooked' is an anagram indicator.
'politician' becomes 'mp'.
'entering' is an insertion indicator.
'oily' is an anagram of 'olyi'.
'olyi' placed around 'mp' is 'olympi'.
'olympi'+'a'='OLYMPIA'
(Other definitions for olympia that I've seen before include "Greek district" , "plain in Greece" , "A place to exhibit" , "Scene of the original games" , "West London exhibition venue - Washington state capital" .)