The most common and most likely answer to this crossword clue is the 9 letter word FRUITCAKE
I've seen this crossword clue in The Times
F
R
U
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T
C
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Buddy explains!
The straight part
We know that "Eccentric/offering of a tea shop" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eccentric/offering of a tea shop = fruitcake.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.
What does FRUITCAKE mean?
FRUITCAKE noun- A cake containing dried fruits and, optionally, nuts, citrus peel and spice.
- A crazy or eccentric person.
- A homosexual male.