Baltic citizen taking son out of posh school? (7)
I believe the answer is:
etonian
'of posh school?' is the definition.
(relating to Eton, English public school)
'baltic citizen taking son' is the wordplay.
'baltic citizen' becomes 'Estonian' (Estonia is a Baltic nation).
'taking' indicates named letters should be taken away.
'son' becomes 's' (genealogical abbreviation for son).
'estonian' with 's' removed is 'ETONIAN'.
'out' is the link.
This may not be right. It may be part of another bit of the clue.
(Other definitions for etonian that I've seen before include "Public school boy" , "Relating to one particular school" , "Public schoolboy" , "Pupil at posh English school" , "One educated at famous public school" .)