Swedish group vacated cosy monastery office (6)
I believe the answer is:
'monastery office' is the definition.
(I've seen this in another clue)
'swedish group vacated cosy' is the wordplay.
'swedish group' becomes 'abba' (I've seen this before).
'vacated' suggests removing the centre.
'cosy' with its middle taken out is 'cy'.
(Other definitions for abbacy that I've seen before include "Office of the head of a religious house", "Jurisdiction of a Father Superior", "Office of the head of a monastery", "ecclesiastical office", "Office of an abbot".)