Lector is moving religious residence (8)
I believe the answer is:
cloister
'religious residence' is the definition.
('cloister' can be a synonym of 'religious residence')
'lector is moving' is the wordplay.
'moving' is an anagram indicator.
'lector'+'is'='lectoris'
'lectoris' anagrammed gives 'CLOISTER'.
(Other definitions for cloister that I've seen before include "Covered walk in monastery or convent" , "sacred enclosure?" , "Walkway round church etc" , "ambulatory" , "Covered walk along the side of a monastery" .)