Function of list, reportedly (4)
I believe the answer is:
role
'function' is the definition.
('role' can be a synonym of 'function')
'list reportedly' is the wordplay.
'list' becomes 'roll' (roll is a kind of list).
'reportedly' indicates a 'sounds like' (homophone) clue.
'roll' sounds like 'ROLE'.
'of' is the link.
(Other definitions for role that I've seen before include "Acting part" , "Stage part" , "Actor's part" , "Character" , "Part (in drama)" .)