A centre in the production of fruit (9)
I believe the answer is:
nectarine
'fruit' is the definition.
(I know that nectarine is a fruit)
'a centre in the production' is the wordplay.
'the production' is an anagram indicator.
'a'+'centre'+'in'='acentrein'
'acentrein' anagrammed gives 'NECTARINE'.
'of' acts as a link.
(Other definitions for nectarine that I've seen before include "Luscious fruit" , "Variety or mutation of a peach" , "fruity" , "Entrance I make with thin-skinned peach" , "Peach-like fruit" .)