Store fat with some hesitation (6)
I believe the answer is:
larder
'store' is the definition.
(food store)
'fat with some hesitation' is the wordplay.
'fat' becomes 'lard' (lard is a kind of fat).
'with' means one lot of letters go next to another.
'some hesitation' becomes 'er' (sound used when hesitating).
'lard'+'er'='LARDER'
(Other definitions for larder that I've seen before include "Stock of provisions" , "Cupboard or small room for food" , "Food store" , "Small room for storing food" , "Buttery" .)