The most common and most likely answer to this crossword clue is the 7 plus 8 letter word BENEATH CONTEMPT
I've seen this crossword clue in The Guardian
B
E
N
E
A
T
H
C
O
N
T
E
M
P
T
More clues leading to the result BENEATH CONTEMPT
Buddy explains!
The straight part
We know that "Despicable" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case despicable = beneath contempt.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.