Fat monarch gets food supply (6)
I believe the answer is:
larder
'food supply' is the definition.
(larder is a kind of food supply)
'fat monarch' is the wordplay.
'fat' becomes 'lard' (I've seen this before).
'monarch' becomes 'er' (abbreviation for Elizabeth Regina).
'lard'+'er'='LARDER'
'gets' acts as a link.
(Other definitions for larder that I've seen before include "Food store" , "Buttery" , "Store cupboard" , "Pantry" , "Room or cupboard for storing food" .)