European state slipping into sea (7)
I believe the answer is:
estonia
'european state' is the definition.
(country in Europe)
'slipping into sea' is the wordplay.
'slipping' is an anagram indicator.
'into'+'sea'='intosea'
'intosea' is an anagram of 'ESTONIA'.
(Other definitions for estonia that I've seen before include "European country, capital Tallinn" , "East European country" , "Baltic state" , "Republic in the Baltic region, once part of USSR" , "'So eat in here in Tallinn, say (7)'" .)