The most common and most likely answer to this crossword clue is the 5 plus 5 plus 1 letter word SWINE FEVER P
I've seen this crossword clue in The Daily Telegraph
S
W
I
N
E
F
E
V
E
R
P
Buddy explains!
The straight part
We know that "beastly complaint" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case beastly complaint = swine fever p.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.