The most common and most likely answer to this crossword clue is the 5 plus 2 plus 7 letter word HOUSE OF WINDSOR
I've seen this crossword clue in The Daily Telegraph
H
O
U
S
E
O
F
W
I
N
D
S
O
R
Buddy explains!
The straight part
We know that "Royal family" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case royal family = house of windsor.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.