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' means one lot of letters goes inside another.
'prig' put within 'cult' is 'culprigt'.
'culprigt' with 'g' taken away is 'CULPRIT'.
(Other definitions for culprit that I've seen before include "Criminal" , "baddie" , "Offender or guilty party" , "he should have conviction" , "Wrongdoer" .)