No-good prig in cult: who’s to blame? (7)
I believe the answer is:
culprit
'who's to blame?' is the definition.
(the culprit is the person to blame)
'no-good prig in cult' is the wordplay.
'no' is a deletion indicator.
'good' becomes 'g' (abbreviation).
'in' is an insertion indicator.
'prig' going within 'cult' is 'culprigt'.
'culprigt' with 'g' removed is 'CULPRIT'.
(Other definitions for culprit that I've seen before include "The one to blame, guilty party" , "he should have conviction" , "The person to blame, the guilty one" , "Offender or guilty party" , "baddie" .)