Group vacated Coventry to establish religious office (6)
I believe the answer is:
abbacy
'religious office' is the definition.
(I've seen this in another clue)
'group vacated coventry' is the wordplay.
'group' becomes 'ABBA' (pop group).
'vacated' says to hollow out the word (remove centre letters) (internal letters vacate the word).
'coventry' with its centre taken out is 'cy'.
'abba'+'cy'='ABBACY'
'to establish' acts as a link.
(Other definitions for abbacy that I've seen before include "Jurisdiction of a Father Superior" , "Office of the head of a monastery" , "Office of senior monk" , "Office of an abbot" , "ecclesiastical office" .)