The most common and most likely answer to this crossword clue is the 3 plus 4 plus 3 plus 4 letter word LET THEM EAT CAKE
I've seen this crossword clue in Financial Times
L
E
T
T
H
E
M
E
A
T
C
A
K
E
More clues leading to the result LET THEM EAT CAKE
Buddy explains!
The straight part
We know that "It shows contempt" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it shows contempt = let them eat cake.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.