Cryptic crossword clue
Tiles in a teashop, broken, top of roof having fallen in 5,4

The most common and most likely answer to this crossword clue is the 5 plus 4 letter word OPERA HATS

I've seen this crossword clue in The Daily Telegraph
O
P
E
R
A
H
A
T
S

Buddy explains!

The straight part
We know that "Tiles" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tiles = opera hats.
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.

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