Regret that could make me sorer (7)
I believe the answer is:
remorse
'regret' is the definition.
(remorse is a feeling of regret)
'could make me sorer' is the wordplay.
'could make' is an anagram indicator.
'me'+'sorer'='mesorer'
'mesorer' with letters rearranged gives 'REMORSE'.
'that' acts as a link.
(Other definitions for remorse that I've seen before include "Pangs of conscience" , "Regret for wrong" , "Gnawing pain of conscience" , "Sorrow for wrongs committed" , "Sorrow for sin or wrong-doing" .)