State's serial criminal (6)
I believe the answer is:
israel
'state's' is the definition.
(Israel is an example)
'serial criminal' is the wordplay.
'criminal' is an anagram indicator.
'serial' anagrammed gives 'ISRAEL'.
(Other definitions for israel that I've seen before include "Serial about Jewish nation" , "Eastern Mediterranean country" , "Strange serial state" , "Zion" , "Hands perhaps" .)