The most common and most likely answer to this crossword clue is the 11 letter word SERENDIPITY
I've seen this crossword clue in The Daily Telegraph
S
E
R
E
N
D
I
P
I
T
Y
Buddy explains!
The straight part
We know that "happy coincidence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case happy coincidence = serendipity.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 SERENDIPITY mean?
SERENDIPITY noun- A combination of events which have come together by chance to make a surprisingly good or wonderful outcome.
- An unsought, unintended, and/or unexpected, but fortunate, discovery and/or learning experience that happens by accident.