The most common and most likely answer to this crossword clue is the 6 letter word SQUASH
I've seen this crossword clue in The Guardian
S
Q
U
A
S
H
Buddy explains!

The straight part
We know that "court activity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case court activity = squash.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 SQUASH mean?
SQUASH noun- A sport played in a walled court with a soft rubber ball and bats like tennis racquets.
- A soft drink made from a fruit-based concentrate diluted with water.
- A place or a situation where people have limited space to move.
- Something soft and easily crushed; especially, an unripe pod of peas.
- Something unripe or soft.
- A sudden fall of a heavy, soft body; also, a shock of soft bodies.
- An extremely one-sided, usually short, match.
- To beat or press into pulp or a flat mass; to crush.
- To compress or restrict (oneself) into a small space; to squeeze.
- To suppress; to force into submission.
- A plant and its fruit of any of a few species of the genus Cucurbita, or gourd kind.
- Any other similar-looking plant of other genera.
- The edible or decorative fruit of these plants, or this fruit prepared as a dish.
- Muskrat.