The most common and most likely answer to this crossword clue is the 11 letter word AGRICULTURE
I've seen this crossword clue in Independent
A
G
R
I
C
U
L
T
U
R
E
More clues leading to the result AGRICULTURE
Buddy explains!

The straight part
We know that "Activity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case activity = agriculture.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 AGRICULTURE mean?
AGRICULTURE noun- The art or science of cultivating the ground, including the harvesting of crops, and the rearing and management of livestock