The most common and most likely answer to this crossword clue is the 8 plus 7 letter word BALLROOM DANCING
I've seen this crossword clue in The Daily Telegraph
B
A
L
L
R
O
O
M
D
A
N
C
I
N
G
Buddy explains!
The straight part
We know that "recreational activity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case recreational activity = ballroom dancing.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.