Fighter lost heart, turning to key supplier of fruit (3,4)

I believe the answer is:

fig tree

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'supplier of fruit' is the definition.
The answer and definition can be both plants as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'fighter lost heart turning to key' is the wordplay.
'lost heart' suggests removing the centre.
'turning to' is an anagram indicator (the letters can turn into other words).
'key' becomes 'E' (musical key).
'fighter' with its centre removed is 'figter'.
'figter' anagrammed gives 'figtre'.
'figtre'+'e'='FIG-TREE'

Can you help me to learn more?

(Other definitions for fig tree that I've seen before include "Leaves producer" , "Get fire (anag)" , "original costume supplier" .)

I've seen this clue in The Daily Express.

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