The most common and most likely answer to this crossword clue is the 4 letter word TEST
I've seen this crossword clue in The Times
T
E
S
T
More clues leading to the result TEST
- After half-term, extremely short exam
- Irritable when not finishing exam
- Bit of smoke's back in top piece of lab kit
- Trial match
- Up-to-the-minute news excluding the French sporting event
- Analyse water flowing through Hampshire
- ... at first this is in Paris Match
- Assessedoutside of the standard range
- Examination taken by postgraduate students?
- Evacuate the street in dry run
Buddy explains!

The straight part
We know that "You can run after driving in this sporting event" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case you can run after driving in this sporting event = test.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 TEST mean?
TEST noun- A challenge, trial.
- A cupel or cupelling hearth in which precious metals are melted for trial and refinement.
- (academia) An examination, given often during the academic term.
- A session in which a product or piece of equipment is examined under everyday or extreme conditions to evaluate its durability, etc.
- (normally “Test”) A Test match.
- The external calciferous shell, or endoskeleton, of an echinoderm, e.g. sand dollars and sea urchins.
- Testa; seed coat.
- Judgment; distinction; discrimination.
- To challenge.
- To refine (gold, silver, etc.) in a test or cupel; to subject to cupellation.
- To put to the proof; to prove the truth, genuineness, or quality of by experiment, or by some principle or standard; to try.
- (academics) To administer or assign an examination, often given during the academic term, to (somebody).
- To place a product or piece of equipment under everyday and/or extreme conditions and examine it for its durability, etc.
- To be shown to be by test.
- To examine or try, as by the use of some reagent.
- A witness.
- To attest (a document) legally, and date it.
- To make a testament, or will.
- (body building) testosterone