Filbert's leaving Burma entering Chinese republic (3,6)
I believe the answer is:
san marino
'republic' is the definition.
(San Marino is a European country)
'filbert's leaving burma entering chinese' is the wordplay.
'filbert's' becomes 'my' (where the crossword setter is 'Filbert').
'leaving' indicates named letters should be taken away.
'burma' becomes 'Myanmar' (synonyms).
'entering' indicates putting letters inside.
'chinese' becomes 'sino' (prefix meaning 'Chinese').
'myanmar' with 'my' removed is 'anmar'.
'anmar' going inside 'sino' is 'SAN MARINO'.
(Other definitions for san marino that I've seen before include "Small independent republic in NE Italy" , "town in Northern Italy" , "European microstate" , "Europe's smallest republic" , "No marinas in this small Italian republic" .)