Left by part of church, daughter fell from the faith (6)
I believe the answer is:
lapsed
'fell from the faith' is the definition.
'left by part of church daughter' is the wordplay.
'left' becomes 'l' (common abbreviation).
'by' says to put letters next to each other.
'part of church' becomes 'apse' ('apse' is part of 'church').
'daughter' becomes 'd'.
'l'+'apse'+'d'='LAPSED'
(Other definitions for lapsed that I've seen before include "Expired, ran out" , "Out of date" , "Became invalid (through lack of renewal)" , "Pleads, having failed to maintain standards" , "Expired over pedals" .)