The most common and most likely answer to this crossword clue is the 4 plus 6 letter word SALT CELLAR
S
A
L
T
C
E
L
L
A
R
Buddy explains!
The straight part
We know that "half of a dining set" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case half of a dining set = salt cellar.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.