I'm taken aback after European initially gave cost to settle abroad (8)
I believe the answer is:
emigrate
'to settle abroad' is the definition.
'i'm taken aback after european initially gave cost' is the wordplay.
'taken aback' says the letters should be written backwards.
'after' says to put letters next to each other.
'european' becomes 'e' (abbreviation e.g. EU).
'initially' says to take the initial letters.
'cost' becomes 'rate' (rate is a kind of cost**).
The first letter of 'gave' is 'g'.
'im' written backwards gives 'mi'.
'mi' put after 'e' is 'emi'.
'emi'+'g'+'rate'='EMIGRATE'
(Other definitions for emigrate that I've seen before include "Gear item (anag.)" , "don't come back!" , "Leave the country to settle abroad" , "Go to settle in a foreign country" , "Leave to settle in another country" .)