The most common and most likely answer to this crossword clue is the 7 plus 4 plus 4 letter word FEATHER ONES NEST
I've seen this crossword clue in The Sunday Telegraph
F
E
A
T
H
E
R
O
N
E
S
N
E
S
T
More clues leading to the result FEATHER ONES NEST
Buddy explains!
The straight part
We know that "Clean up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case clean up = feather ones nest.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.