The most common and most likely answer to this crossword clue is the 3 plus 3 plus 3 letter word HUE AND CRY
I've seen this crossword clue in The Times
H
U
E
A
N
D
C
R
Y
More clues leading to the result HUE AND CRY
- Alternative cure handy for major complaint
- A criminal pursuit, something shady with opening of cocaine lines
- C can dry out, leading to public outburst
- Tint with blubber, leading to commotion
- Noisy protest extremely unchristian — head dished out a hundred lines
- Raunchy, semi-nude dancing creates uproar
- Furore breaking under 5
- Loud clamour exploding near duchy
- Loud racket may lead to apprehension
- The chase that’s on for handy cure to be developed?
Buddy explains!

The straight part
We know that "major complaint" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case major complaint = hue and cry.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.