The most common and most likely answer to this crossword clue is the 5 plus 7 letter word ELVIS PRESLEY
I've seen this crossword clue in The Guardian
E
L
V
I
S
P
R
E
S
L
E
Y
More clues leading to the result ELVIS PRESLEY
Buddy explains!
The straight part
We know that "Icon" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case icon = elvis presley.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.