A firm one Irishman raised producing pudding (7)
I believe the answer is:
tapioca
'pudding' is the definition.
(tapioca pudding is a kind of pudding)
'a firm one irishman raised' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'one' becomes 'i' (Roman numeral).
'irishman' becomes 'pat'.
'raised' says the letters should be written in reverse.
'a'+'co'+'i'+'pat'='acoipat'
'acoipat' backwards is 'TAPIOCA'.
'producing' is the link.
(Other definitions for tapioca that I've seen before include "Pudding thickener" , "Pudding from the cassava root" , "dessert" , "I act OAP (anag) - edible substance made from cassava" , "course" .)