Two companions going around old city building (6)
I believe the answer is:
church
'building' is the definition.
(I know that church is a type of temple)
'two companions going around old city' is the wordplay.
'two companions' means two replacements for 'companion'.
'companion' becomes 'ch' (Companion of Honour).
'companion' becomes 'ch' (Companion of Honour).
'going around' is an insertion indicator.
'old city' becomes 'ur' (ancient Sumerian city state).
'ch'+'ch'='chch'
'chch' going around 'ur' is 'CHURCH'.
(Other definitions for church that I've seen before include "A building for Christian worship" , "fold" , "Holy establishment" , "Ecclesiastical building" , "Building for religious worship" .)