The most common and most likely answer to this crossword clue is the 11 letter word FLY-TIPPING
I've seen this crossword clue in The Times
F
L
Y
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T
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P
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G
More clues leading to the result FLY-TIPPING
Buddy explains!

The straight part
We know that "unauthorised dispatch" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unauthorised dispatch = fly-tipping.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 FLY-TIPPING mean?
FLY-TIPPING verb- To dispose of waste (garbage) illegally, rather than at an authorized dump location.
- The illegal dumping of rubbish on unauthorised sites.