The most common and most likely answer to this crossword clue is the 2 plus 3 plus 3 letter word ON THE RUN
I've seen this crossword clue in The Daily Telegraph
O
N
T
H
E
R
U
N
More clues leading to the result ON THE RUN
- In Piedmont, her uncle's trying to avoid capture
- Alternative international body pinching name wanted by police?
- Possibly topless May Queen, one being pursued
- Trying to escape joining in a marathon?
- Number put up hunter in disguise, avoiding arrest?
- Like fugitives, one after the other
- Fugitive ahead perplexed hunter
- None hurt badly in retreat
- No hunter is disturbed when being chased
- Fleeing, one after another?
Buddy explains!

The straight part
We know that "Fleeing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fleeing = on the run.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.