Church recently admitting single Bishop's chaste (8)
I believe the answer is:
celibate
'chaste' is the definition.
('celibate' can be similar in meaning to 'chaste')
'church recently admitting single bishop's' is the wordplay.
'church' becomes 'ce' (abbreviation for Church of England).
'recently' becomes 'late' (I've seen this in other clues).
'admitting' is an insertion indicator.
'single' becomes 'i' (one).
'bishop' becomes 'b' (abbreviation used in chess).
'i'+'b'='ib'
'late' enclosing 'ib' is 'libate'.
'ce'+'libate'='CELIBATE'
(Other definitions for celibate that I've seen before include "Refraining from sex" , "Not the marrying kind" , "Belie act of being voluntarily chaste" , "Continent" , "Citeable as unmarried for religious reasons" .)