Some err, possibly, showing shame (7)
I believe the answer is:
remorse
'shame' is the definition.
(thesaurus)
'some err possibly' is the wordplay.
'possibly' is an anagram indicator.
'some'+'err'='someerr'
'someerr' anagrammed gives 'REMORSE'.
'showing' is the link.
(Other definitions for remorse that I've seen before include "Bitter regret" , "Regret or sorrow for wrong-doing" , "Sorrow for wrongs committed" , "Self-reproach" , "regrets" .)