The most common and most likely answer to this crossword clue is the 12 letter word EVEN-STEVENS
I've seen this crossword clue in The Times
E
V
E
N
-
S
T
E
V
E
N
S
More clues leading to the result EVEN-STEVENS
Buddy explains!
The straight part
We know that "Quits" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quits = even-stevens.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 EVEN-STEVENS mean?
EVEN-STEVENS noun- An equal situation, in which no side has an advantage