The most common and most likely answer to this crossword clue is the 9 letter word UNEXPIRED
I've seen this crossword clue in The Times
U
N
E
X
P
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D
More clues leading to the result UNEXPIRED
Buddy explains!

The straight part
We know that "still running" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case still running = unexpired.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 UNEXPIRED mean?
UNEXPIRED adjective- Not having expired.
- Of food: not having reached its expiry date.
- Of an agreement, coupon, or law, still in force.