The most common and most likely answer to this crossword clue is the 4 plus 7 letter word JERK CHICKEN
I've seen this crossword clue in The Guardian
J
E
R
K
C
H
I
C
K
E
N
More clues leading to the result JERK CHICKEN
Buddy explains!

The straight part
We know that "Table for a Jamaican" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case table for a jamaican = jerk chicken.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.