The most common and most likely answer to this crossword clue is the 7 letter word STEAMED
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More clues leading to the result STEAMED
Buddy explains!

The straight part
We know that "moved quickly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moved quickly = steamed.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 STEAMED mean?
STEAMED verb- To cook with steam.
- To expose to the action of steam; to apply steam to for softening, dressing, or preparing.
- To produce or vent steam.
- To rise in vapour; to issue, or pass off, as vapour.
- To become angry; to fume; to be incensed.
- To make angry.
- To be covered with condensed water vapor.
- To travel by means of steam power.
- To move with great or excessive purposefulness.
- To exhale.
- Cooked by steaming.
- Angry, hot under the collar.