Fail to notice finished appearance (8)
I believe the answer is:
overlook
'fail to notice' is the definition.
(I've seen this before)
'finished appearance' is the wordplay.
'finished' becomes 'over' ('over' can be similar in meaning to 'finished').
'appearance' becomes 'look' (look is a kind of appearance**).
'over'+'look'='OVERLOOK'
(Other definitions for overlook that I've seen before include "Ignore a fault or have a view from above" , "Ignore or fail to see" , "Ignore or fail to notice" , "Fail to observe or consider" , "Keep an eye on" .)