The most common and most likely answer to this crossword clue is the 9 letter word STUMBLING
I've seen this crossword clue in The Times
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Buddy explains!
The straight part
We know that "Moving unsteadily" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moving unsteadily = stumbling.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 STUMBLING mean?
STUMBLING verb- To trip or fall; to walk clumsily.
- To make a mistake or have trouble.
- To cause to stumble or trip.
- To mislead; to confound; to cause to err or to fall.
- To strike or happen (upon a person or thing) without design; to fall or light by chance; with on, upon, or against.
- The motion of one who stumbles.