The most common and most likely answer to this crossword clue is the 3 plus 1 plus 5 plus 5 letter word ITS A SMALL WORLD
I've seen this crossword clue in The Times
I
T
S
A
S
M
A
L
L
W
O
R
L
D
More clues leading to the result ITS A SMALL WORLD
Buddy explains!

The straight part
We know that "Fancy seeing you" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fancy seeing you = its a small world.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.