The most common and most likely answer to this crossword clue is the 11 letter word VINDICATION
I've seen this crossword clue in The Daily Telegraph
V
I
N
D
I
C
A
T
I
O
N
More clues leading to the result VINDICATION
Buddy explains!

The straight part
We know that "support" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case support = vindication.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.
What does VINDICATION mean?
VINDICATION noun- The act of vindicating or the state of being vindicated.
- Evidence, facts, statements, or arguments that justify a claim or belief.