The most common and most likely answer to this crossword clue is the 9 letter word MIGRATING
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Buddy explains!

The straight part
We know that "on the move" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on the move = migrating.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 MIGRATING mean?
MIGRATING verb- To relocate periodically from one region to another, usually according to the seasons.
- To change one's geographic pattern of habitation.
- To change habitations across a border; to move from one country or political region to another.
- To move slowly towards, usually in groups.
- : To move computer code or files from one computer or network to another.
- To induce customers to shift purchases from one set of a company's related products to another.