The most common and most likely answer to this crossword clue is the 8 letter word ALLEGROS
I've seen this crossword clue in Financial Times
A
L
L
E
G
R
O
S
More clues leading to the result ALLEGROS
Buddy explains!

The straight part
We know that "Speedy movements" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case speedy movements = allegros.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 ALLEGROS mean?
ALLEGROS noun- A tempo mark directing that a passage is to be played in a quick, lively tempo, faster than allegretto but slower than presto
- In more traditional use, an expressive marking indicating lively or happily, not necessarily quick or fast.
- A passage having this mark