Aspired to include part of church (5)
I believe the answer is:
spire
'part of church' is the definition.
'aspired to include' is the wordplay.
'to include' indicates the answer is hidden within the clue.
'SPIRE' is hidden within 'aspired'.
(Other definitions for spire that I've seen before include "feature of high church?" , "Crooked feature in Chesterfield" , "Tall pointed structure as on church or in O'Connell St." , "one over the church?" , "Tall cone-shaped structure on church" .)