The most common and most likely answer to this crossword clue is the 4 plus 5 letter word MOCK TUDOR
I've seen this crossword clue in Independent
M
O
C
K
T
U
D
O
R
More clues leading to the result MOCK TUDOR
Buddy explains!

The straight part
We know that "ye olde style" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ye olde style = mock tudor.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.