Conspire with saintly bishop, a debt to resolve (3,3,4)
I believe the answer is:
aid and abet
'conspire with' is the definition.
(to aid and abet someone is to conspire with them)
'saintly bishop a debt to resolve' is the wordplay.
'saintly bishop' becomes 'Aidan' (Saint Aidan, 7th-century bishop).
'to resolve' is an anagram indicator (I've seen 'resolved' mean this).
'adebt' anagrammed gives 'dabet'.
'aidan'+'dabet'='AID AND ABET'