The most common and most likely answer to this crossword clue is the 8 plus 6 letter word BLENHEIM PALACE
I've seen this crossword clue in The Times
B
L
E
N
H
E
I
M
P
A
L
A
C
E
More clues leading to the result BLENHEIM PALACE
Buddy explains!
The straight part
We know that "Stately home" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stately home = blenheim palace.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.