Part of Provence that cooks (4)
I believe the answer is:
oven
'that cooks' is the definition.
(ovens cook food)
'part of provence' is the wordplay.
'part of' indicates a hidden word.
'OVEN' can be found hidden inside 'provence'.
(Other definitions for oven that I've seen before include "Kiln, cooker" , "Small kiln" , "Section of a cooker" , "Chamber for baking" , "Cooker; furnace" .)