Hat-wearing convict shows cultivation (7)
I believe the answer is:
tillage
'cultivation' is the definition.
(I know that tillage is a type of culture)
'hat-wearing convict' is the wordplay.
'hat' becomes 'tile' (old-fashioned term for a hat).
'wearing' means one lot of letters goes inside another.
'convict' becomes 'lag' (slang term for a prisoner).
'tile' placed around 'lag' is 'TILLAGE'.
'shows' acts as a link.
(Other definitions for tillage that I've seen before include "Farmers work at it" , "Cultivation of the soil" , "Cultivation of the land" , "digging" , "Cultivated land" .)