The most common and most likely answer to this crossword clue is the 9 letter word UNDERGIRD
U
N
D
E
R
G
I
R
D
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 = undergird.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 UNDERGIRD mean?
UNDERGIRD verb- To strengthen, secure, or reinforce by passing a rope, cable, or chain around the underside of an object.
- To give fundamental support; provide with a sound or secure basis; provide supportive evidence for.
- To lend moral support to.
- To secure below or underneath.