The most common and most likely answer to this crossword clue is the 11 letter word CONSUMMATED
I've seen this crossword clue in The Times
C
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Buddy explains!

The straight part
We know that "Finished" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case finished = consummated.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CONSUMMATED mean?
CONSUMMATED verb- To bring (a task, project, goal etc.) to completion; to accomplish.
- To make perfect, achieve, give the finishing touch.
- To make (a marriage) complete by engaging in first sexual intercourse.
- To become perfected, receive the finishing touch.