The most common and most likely answer to this crossword clue is the 11 letter word BOOTLEGGING
I've seen this crossword clue in The Times
B
O
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More clues leading to the result BOOTLEGGING
Buddy explains!

The straight part
We know that "Illegally disposing of" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case illegally disposing of = bootlegging.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 BOOTLEGGING mean?
BOOTLEGGING verb- To make, transport and/or sell illegal alcoholic liquor.
- To make, transport and/or sell an illegal version or copy of a copyrighted product.
- To engage in bootlegging.