The most common and most likely answer to this crossword clue is the 4 plus 7 letter word WIND TURBINE
I've seen this crossword clue in The Daily Telegraph
W
I
N
D
T
U
R
B
I
N
E
Buddy explains!
The straight part
We know that "Victory over brute whirling with din — for Nimbys opposing it" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case victory over brute whirling with din — for nimbys opposing it = wind turbine.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.