Putting bible back, I can't suspect authority of church (7)
I believe the answer is:
vatican
'authority of church' is the definition.
(city state home to the Pope)
'putting bible back i can't suspect' is the wordplay.
'putting bible back' becomes 'va' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'suspect' is an anagram indicator.
'i'+'cant'='icant'
'icant' with letters rearranged gives 'tican'.
'va'+'tican'='VATICAN'
(Other definitions for vatican that I've seen before include "Palace of the popes in Rome" , "Papal authority" , "Papal hill and city" , "European state" , "Papacy" .)