Aspired to contain part of church (5)
I believe the answer is:
spire
'part of church' is the definition.
'aspired to contain' is the wordplay.
'to contain' indicates a hidden word (I've seen 'contains' mean this).
'SPIRE' is hidden in the letters of 'aspired'.
(Other definitions for spire that I've seen before include "Piers (anag.)" , "feature of high church?" , "Tall pointed structure as on church or in O'Connell St." , "Feature of many churches" , "Pointed church tower" .)