The most common and most likely answer to this crossword clue is the 7 letter word FLY-TIP
I've seen this crossword clue in Independent
F
L
Y
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More clues leading to the result FLY-TIP
Buddy explains!

The straight part
We know that "dump" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dump = fly-tip.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.
Crossword Answer definitions
FLY-TIP noun- A pile of rubbish discarded in such a manner
- To dispose of waste (garbage) illegally, rather than at an authorized dump location.