The most common and most likely answer to this crossword clue is the 6 plus 7 letter word AUGEAN STABLES
I've seen this crossword clue in The Times
A
U
G
E
A
N
S
T
A
B
L
E
S
Buddy explains!
The straight part
We know that "that Labour cleaned out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that labour cleaned out = augean stables.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.