Shakespearean carpenter, fruity thing (6)

I believe the answer is:

quince

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This could be a double definition.

'shakespearean carpenter' is the first definition.
'quince' can be an answer for 'carpenter' (I've seen this before). I am not sure about the 'shakespearean' bit.

'fruity thing' is the second definition.
(type of fruit)

Can you help me to learn more?

(Other definitions for quince that I've seen before include "Acid pear-shaped fruit used in preserves" , "Peter -- (A Midsummer Night's Dream)" , "part-time Athenian dramatist" , "Fruit used to make jam" , "Acidic fruit used in preserves" .)

I've seen this clue in The Telegraph.

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