The most common and most likely answer to this crossword clue is the 3 plus 4 plus 6 letter word CRY BLUE MURDER
I've seen this crossword clue in The Daily Telegraph
C
R
Y
B
L
U
E
M
U
R
D
E
R
Buddy explains!
The straight part
We know that "complain very loudly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case complain very loudly = cry blue murder.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.