Feeling of regret after taking in variable Cornish resort (8)
I believe the answer is:
penzance
'cornish resort' is the definition.
(Penzance is a resort town in Cornwall)
'feeling of regret after taking in variable' is the wordplay.
'feeling of regret' becomes 'penance' (penance is repentance or guilt).
'after taking in' indicates putting letters inside.
'variable' becomes 'z' (algebra).
'penance' enclosing 'z' is 'PENZANCE'.
(Other definitions for penzance that I've seen before include "Pirates of -, (G&S)" , "Cornish town burnt by the Spaniards" , "Resort in Cornwall" , "Whence G&S_pirates" , "pirates' home" .)