The most common and most likely answer to this crossword clue is the 8 letter word UNDERLIE
I've seen this crossword clue in Independent
U
N
D
E
R
L
I
E
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 = underlie.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 UNDERLIE mean?
UNDERLIE verb- To lie in a position directly beneath.
- To lie under or beneath.
- To serve as a basis of; form the foundation of.
- To be subject to; be liable to answer, as a charge or challenge.
- To underlay.