The most common and most likely answer to this crossword clue is the 12 letter word OFF-THE-WALL
O
F
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T
H
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W
A
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More clues leading to the result OFF-THE-WALL
Buddy explains!

The straight part
We know that "Where ineptly hung art may be found/avant-garde" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where ineptly hung art may be found/avant-garde = off-the-wall.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 OFF-THE-WALL mean?
OFF-THE-WALL adjective- Wildly unconventional; bizarre; absurd.
- Of a person's behaviour: greatly inappropriate.