The most common and most likely answer to this crossword clue is the 6 plus 9 letter word SUMMER RESIDENCE
I've seen this crossword clue in Financial Times
S
U
M
M
E
R
R
E
S
I
D
E
N
C
E
Buddy explains!
The straight part
We know that "what the Queen has at Balmoral" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what the queen has at balmoral = summer residence.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.