The most common and most likely answer to this crossword clue is the 9 letter word AIMLESSLY
I've seen this crossword clue in Financial Times
A
I
M
L
E
S
S
L
Y
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The straight part
We know that "without any purpose" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case without any purpose = aimlessly.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 AIMLESSLY mean?
AIMLESSLY adverb- Without an aim, purpose or direction; in an aimless manner.