Last bit of crossword somebody finished (4)
I believe the answer is:
done
'finished' is the definition.
(I've seen this before)
'last bit of crossword somebody' is the wordplay.
'last bit of' says to take the final letters.
'somebody' becomes 'one' (I've seen this in other clues).
The final letter of 'crossword' is 'd'.
'd'+'one'='DONE'
(Other definitions for done that I've seen before include "Robbed" , "This settled" , "Tricked" , "Swindled" , "Complete; finished" .)