Give up right to face European character (6)
I believe the answer is:
letter
'character' is the definition.
(I know that character can be written as letter)
'give up right to face european' is the wordplay.
'give' becomes 'let' (letting is a kind of giving).
'up' indicates an anagram (letters get chucked up).
'face' says to take the initial letters.
'european' becomes 'E' (abbreviation e.g. EU).
The initial letters of 'right to' is 'rt'.
'rt'+'e'='rte'
'rte' anagrammed gives 'ter'.
'let'+'ter'='LETTER'
(Other definitions for letter that I've seen before include "reference?" , "An alphabetic unit" , "Character of the alphabet" , "Item sent - character" , "Written message" .)