Resolved to relieve oil producer (5,4)

I believe the answer is:

olive tree

I'm a little stuck... Click here to teach me more about this clue!

'oil producer' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'resolved to relieve' is the wordplay.
'resolved' indicates an anagram.
'to'+'relieve'='torelieve'
'torelieve' anagrammed gives 'OLIVE TREE'.

Can you help me to learn more?

(Other definitions for olive tree that I've seen before include "oil supplier" , "bearer of fruit" .)

I've seen this clue in The Times.

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