The most common and most likely answer to this crossword clue is the 14 letter word UNFLAPPABILITY
I've seen this crossword clue in The Times
U
N
F
L
A
P
P
A
B
I
L
I
T
Y
More clues leading to the result UNFLAPPABILITY
Buddy explains!
The straight part
We know that "Composure/lack of power in broken wings?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case composure/lack of power in broken wings? = unflappability.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.