With flattery, talk round Eastern European living in desperation (8)
I believe the answer is:
inveigle
'with flattery talk round' is the definition.
(to inveigle is to persuade or flatter)
'eastern european living in desperation' is the wordplay.
'eastern' becomes 'e'.
'european' becomes 'E' (abbreviation e.g. EU).
'in desperation' indicates anagramming the letters (a desperate spelling).
'e'+'e'+'living'='eeliving'
'eeliving' with letters rearranged gives 'INVEIGLE'.
(Other definitions for inveigle that I've seen before include "Induce by trick, cajole" , "Persuade by flattery" , "Lead on, entice" , "Seduce" , "Persuade by deception" .)