The most common and most likely answer to this crossword clue is the 6 letter word MOPTOP
I've seen this crossword clue in Financial Times
M
O
P
T
O
P
Buddy explains!

The straight part
We know that "Beatle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case beatle = moptop.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 MOPTOP mean?
MOPTOP noun- A style of haircut popularized by the Beatles