Cockney’s aim to be admitted to feast (4,5)
I believe the answer is:
east ender
'cockney's' is the definition.
(I've seen this before)
'aim to be admitted to feast' is the wordplay.
'aim' becomes 'end' (both can mean a goal or purpose).
'to be admitted to' is an insertion indicator.
'feast' becomes 'easter' (I've seen this before).
'end' going into 'easter' is 'EAST-ENDER'.
(Other definitions for east ender that I've seen before include "Cockney" , "Citizen" , "Someone born within the sound of Bow Bells?" , "City dweller" , "TV character" .)