The most common and most likely answer to this crossword clue is the 9 letter word PATRONESS
I've seen this crossword clue in The Times
P
A
T
R
O
N
E
S
S
Buddy explains!

The straight part
We know that "supporter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supporter = patroness.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 PATRONESS mean?
PATRONESS noun- A woman who sponsors or supports a given activity, person etc.; a female patron.
- To support or sponsor as a patroness.