The most common and most likely answer to this crossword clue is the 6 plus 3 letter word CONGER EEL
I've seen this crossword clue in Independent
C
O
N
G
E
R
E
E
L
Buddy explains!
The straight part
We know that "caught – gone off to dance (6,3)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case caught – gone off to dance (6,3) = conger eel.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.