Earlier religious building, incomplete (5)
I believe the answer is:
prior
'earlier' is the definition.
('prior' can be a synonym of 'earlier')
'religious building incomplete' is the wordplay.
'religious building' becomes 'priory'.
'incomplete' means to remove the last letter.
'priory' with its last letter taken away is 'PRIOR'.
(Other definitions for prior that I've seen before include "Former - cleric" , "Earlier, coming before another in time" , "Coming before N a superior" , "Previous; abbot's deputy" , "Antecedent" .)