The most common and most likely answer to this crossword clue is the 4 plus 2 plus 3 plus 4 letter word BACK IN THE USSR
I've seen this crossword clue in The Guardian
B
A
C
K
I
N
T
H
E
U
S
S
R
Buddy explains!
The straight part
We know that "Number of the Beatles" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case number of the beatles = back in the ussr.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.