Name of female oil producer (5)
I believe the answer is:
olive
This clue is a triple definition!
'name' is the first definition.
'of' is a link.
'female' is the second definition.
(I've seen this before)
'oil producer' is the third definition.
(I've seen this in another clue)
(Other definitions for olive that I've seen before include "Source of edible oil" , "Oil-producing fruit" , "Yellowish-green - fruit" , "girl" , "This branch is offered to show peace" .)