The most common and most likely answer to this crossword clue is the 5 letter word RACER
I've seen this crossword clue in The Times
R
A
C
E
R
More clues leading to the result RACER
- Athlete runs behind lots of people
- Young greyhound, perhaps — one kept by king and queen
- Competitor — one in luxury car...
- Fast driver expert in Rolls-Royce
- Fast mover runs and runs around expert
- Runner beginning to run, one runs!
- One hurrying about to get vehicle reversing
- Fast mover runs to left of maple tree
- Runner, one between two runs
- Fast driver, expert in Rolls Royce initially
Buddy explains!

The straight part
We know that "Fast mover" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fast mover = racer.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 RACER mean?
RACER noun- Someone who takes part in a race.
- A racehorse.
- An animal known for its fast speed, or suitable for racing; applied especially to a number of North American snakes, certain kinds of lake trout, etc.
- A vehicle or other device used for racing.
- Any of several genera of colubrid snakes.
- A video game involving racing of any kind.