Moved flag right onto higher part of church (5,4)
I believe the answer is:
organ loft
'higher part of church' is the definition.
(high-up part of a church)
'moved flag right onto' is the wordplay.
'moved' is an anagram indicator.
'right' becomes 'r' (common abbreviation).
'flag'+'r'+'onto'='flagronto'
'flagronto' with letters rearranged gives 'ORGAN-LOFT'.
(Other definitions for organ loft that I've seen before include "Church musician's gallery" , "Church feature" , "Part of church" .)