The most common and most likely answer to this crossword clue is the 5 plus 2 letter word BREAK UP
I've seen this crossword clue in The Daily Telegraph
B
R
E
A
K
U
P
More clues leading to the result BREAK UP
Buddy explains!

The straight part
We know that "Finish" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case finish = break up.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 BREAK UP mean?
BREAK UP noun- The act of breaking up; disintegration or division.
- The termination of a friendship, or a romantic relationship.
- A loss of emotional control; a breakdown.
- (Alaska and northern Canada) The time of year during which winter ice covering bodies of water disintegrates, or more generally Spring.