The most common and most likely answer to this crossword clue is the 11 letter word WELL-WISHER
I've seen this crossword clue in The Guardian
W
E
L
L
-
W
I
S
H
E
R
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 = well-wisher.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 WELL-WISHER mean?
WELL-WISHER noun- Someone who extends good wishes, or expresses sympathy to someone else.