The most common and most likely answer to this crossword clue is the 7 letter word RIVALRY
I've seen this crossword clue in Independent
R
I
V
A
L
R
Y
More clues leading to the result RIVALRY
Buddy explains!

The straight part
We know that "Vendetta" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vendetta = rivalry.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 RIVALRY mean?
RIVALRY noun- An ongoing relationship between (usually two) rivals who compete for superiority.
- The characteristic of being a rivalrous good, such that it can be consumed or used by only one person at a time.
- Any competition between two or more things or factors.