Unsightly mark on European causing fright (5)
I believe the answer is:
scare
'fright' is the definition.
(scare is a kind of fright)
'unsightly mark on european' is the wordplay.
'unsightly mark' becomes 'scar' (a mark left by an injury).
'on' means one lot of letters go next to another.
'european' becomes 'E' (abbreviation e.g. EU).
'scar'+'e'='SCARE'
'causing' acts as a link.
(Other definitions for scare that I've seen before include "Health worry" , "Startle" , "Frighten or intimidate" , "Frighten, alarm" , "Panic" .)