The most common and most likely answer to this crossword clue is the 6 letter word DIVING
I've seen this crossword clue in Financial Times
D
I
V
I
N
G
More clues leading to the result DIVING
Buddy explains!

The straight part
We know that "sport" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sport = diving.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 DIVING mean?
DIVING verb- To swim under water.
- To jump into water head-first.
- To jump headfirst toward the ground or into another substance.
- To descend sharply or steeply.
- (especially with in) To undertake with enthusiasm.
- To deliberately fall down after a challenge, imitating being fouled, in the hope of getting one's opponent penalised.
- To cause to descend, dunk; to plunge something into water.
- To explore by diving; to plunge into.
- To plunge or to go deeply into any subject, question, business, etc.; to penetrate; to explore.
- The action of the verb to dive in any sense.
- The sport of jumping into water, often acrobatically.
- Descending below the surface of the water to interact with the environment.
- The act of pretending to be tripped or brought to the ground by an opposition player in order to secure a undeserved penalty.
- That or who dives or dive.