Punishment in Cornish town not unknown (7)
I believe the answer is:
penance
'punishment' is the definition.
(penance is a kind of punishment)
'cornish town not unknown' is the wordplay.
'cornish town' becomes 'penzance' (I've seen this before).
'not' is a deletion indicator.
'unknown' becomes 'z' (algebra).
'penzance' with 'z' taken away is 'PENANCE'.
'in' is the link.
(Other definitions for penance that I've seen before include "Punishment for wrongdoing, by religion perhaps" , "act of self-punishment" , "Act of contrition" , "Voluntary self-punishment" , "Punishment for religious wrongdoing" .)