The most common and most likely answer to this crossword clue is the 6 letter word BESTED
B
E
S
T
E
D
Buddy explains!

The straight part
We know that "Won over" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case won over = bested.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 BESTED mean?
BESTED verb- To surpass in skill or achievement.
- To beat in a contest