The most common and most likely answer to this crossword clue is the 7 plus 4 letter word VANESSA BELL
I've seen this crossword clue in Financial Times
V
A
N
E
S
S
A
B
E
L
L
Buddy explains!
The straight part
We know that "Bloomsbury Virginia’s sister" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bloomsbury virginia’s sister = vanessa bell.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.