The most common and most likely answer to this crossword clue is the 7 letter word WAGGING
W
A
G
G
I
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G
Buddy explains!

The straight part
We know that "waving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case waving = wagging.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 WAGGING mean?
WAGGING verb- To swing from side to side, such as of an animal's tail, or someone's head, to express disagreement or disbelief.
- To play truant from school.
- To be in action or motion; to move; progress.
- To go; to depart.
- The motion of something that is wagged.