Old bishop behind society for religious people (7)
I believe the answer is:
oblates
'religious people' is the definition.
(an oblate is a religious person)
'old bishop behind society' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'bishop' becomes 'B' (abbreviation for bishop in chess).
'behind' becomes 'late' (as in behind schedule).
'society' becomes 's' (common abbreviation in names of organisations).
'o'+'b'+'late'+'s'='OBLATES'
'for' is the link.
(Another definition for oblates that I've seen is " Religious types".)