The most common and most likely answer to this crossword clue is the 10 letter word FUMIGATION
I've seen this crossword clue in The Sunday Telegraph
F
U
M
I
G
A
T
I
O
N
Buddy explains!
The straight part
We know that "process of cleaning up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case process of cleaning up = fumigation.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.
What does FUMIGATION mean?
FUMIGATION noun- The act of fumigating, or applying smoke or vapor, as for disinfection.
- Vapor raised in the process of fumigating.