The most common and most likely answer to this crossword clue is the 11 letter word PIGEON-TOED
I've seen this crossword clue in The Guardian
P
I
G
E
O
N
-
T
O
E
D
Buddy explains!
The straight part
We know that "having misdirected supporters" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having misdirected supporters = pigeon-toed.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 PIGEON-TOED mean?
PIGEON-TOED adjective- Having toes that point inwards.