The most common and most likely answer to this crossword clue is the 8 letter word FLEETEST
I've seen this crossword clue in The Sunday Telegraph
F
L
E
E
T
E
S
T
More clues leading to the result FLEETEST
- Escape exam as fast as possible
- Most speedy escape from ordeal
- Do a bunk from exam with maximum speed
- Escape from ordeal with maximum speed
- Best at running exam — left in charge over it
- Quickest run by runner in Hants
- Escape trial with extreme dispatch
- Run away from ordeal most quickly
- Quickest to escape tax
Buddy explains!

The straight part
We know that "Best at running" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case best at running = fleetest.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 FLEETEST mean?
FLEETEST adjective- Swift in motion; light and quick in going from place to place.
- Light; superficially thin; not penetrating deep, as soil.