Refusal to admit someone good is bad (5)
I believe the answer is:
nasty
'is bad' is the definition.
(thesaurus)
'refusal to admit someone good' is the wordplay.
'refusal' becomes 'nay' (archaic word for 'no').
'to admit' is an insertion indicator.
'someone good' becomes 'st' (saint).
'nay' going around 'st' is 'NASTY'.
(Other definitions for nasty that I've seen before include "Vile" , "One who sees the future" , "Disgusting" , "grave" , "Horrid, repugnant" .)