The most common and most likely answer to this crossword clue is the 7 plus 7 plus 6 plus 8 letter word ELVISNT PRESLEY (ELVIS PRESLEY)
I've seen this crossword clue in The Guardian
E
L
V
I
S
N
T
P
R
E
S
L
E
Y
(
E
L
V
I
S
P
R
E
S
L
E
Y
)
Buddy explains!
The straight part
We know that "Very popular musician" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very popular musician = elvisnt presley (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.