The most common and most likely answer to this crossword clue is the 6 plus 6 letter word UNFAIR CHOICE
I've seen this crossword clue in The Daily Telegraph
U
N
F
A
I
R
C
H
O
I
C
E
Buddy explains!
The straight part
We know that "But a brunette winning a beauty contest may not be" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case but a brunette winning a beauty contest may not be = unfair choice.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.