Flag with damage carried by European vessel (7)
I believe the answer is:
earmark
'flag' is the definition.
(both can mean to highlight or label something)
'damage carried by european vessel' is the wordplay.
'damage' becomes 'mar' (marring is a kind of damaging).
'carried by' is an insertion indicator.
'european' becomes 'e' (abbreviation e.g. EU).
'vessel' becomes 'ark' (ark is a kind of vessel).
'e'+'ark'='eark'
'mar' inserted inside 'eark' is 'EARMARK'.
'with' acts as a link.
(Other definitions for earmark that I've seen before include "It identifies the outcome" , "Set aside specifically" , "Designate for a specific purpose" , "reserve for future use" , "Allocate for a purpose" .)