The most common and most likely answer to this crossword clue is the 4 plus 4 plus 4 plus 2 letter word HAVE DONE WITH IT
I've seen this crossword clue in The Daily Telegraph
H
A
V
E
D
O
N
E
W
I
T
H
I
T
Buddy explains!
The straight part
We know that "Finish the whole affair" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case finish the whole affair = have done with it.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.