The most common and most likely answer to this crossword clue is the 8 letter word DESCANTS
I've seen this crossword clue in The Daily Telegraph
D
E
S
C
A
N
T
S
More clues leading to the result DESCANTS
Buddy explains!

The straight part
We know that "Independent airs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case independent airs = descants.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 DESCANTS mean?
DESCANTS noun- A lengthy discourse on a subject.
- A counterpoint melody sung or played above the theme
- To discuss at length.
- To sing or play a descant.