The most common and most likely answer to this crossword clue is the 6 plus 3 plus 6 letter word SETTLE OLD SCORES
I've seen this crossword clue in Financial Times
S
E
T
T
L
E
O
L
D
S
C
O
R
E
S
More clues leading to the result SETTLE OLD SCORES
Buddy explains!
The straight part
We know that "to deal with grudges" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to deal with grudges = settle old scores.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.