The most common and most likely answer to this crossword clue is the 5 letter word STILT
I've seen this crossword clue in The Daily Telegraph
S
T
I
L
T
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 = stilt.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 STILT mean?
STILT noun- Either of two poles with footrests that allow someone to stand or walk above the ground; used mostly by entertainers.
- A tall pillar or post used to support some structure; often above water.
- Any of various wading birds of the genera Himantopus and Cladorhynchus, related to the avocet, that have extremely long legs and long thin bills.
- A crutch.
- The handle of a plough.
- To raise on stilts, or as if on stilts