Encourage hen’s produce (3)
I believe the answer is:
egg
This could be a double definition.
'encourage' is the first definition.
'hen's produce' is the second definition.
The answer and definition can be both things that one consumes for nourishment as well as being singular nouns.
Maybe you can see an association between them that I don't see?
(Other definitions for egg that I've seen before include "Item of food" , "Poultry product" , "Food from a hen" , "Rasher to go with this" , "Poached or boiled?" .)