Poem of the millennium overlooked by church (5)
I believe the answer is:
iliad
'poem' is the definition.
(Iliad is an example)
'millennium overlooked by church' is the wordplay.
'millennium' becomes 'chiliad' (chiliad can mean a thousand years).
'overlooked by' suggests deleting specific letters.
'church' becomes 'ch' (common abbreviation).
'chiliad' with 'ch' removed is 'ILIAD'.
'of the' acts as a link.
(Other definitions for iliad that I've seen before include "Work by Homer" , "Greek epic poem describing the siege of Troy" , "Work on war" , "Greek epic poem about the Trojan War" , "Poem by 4 across" .)