Those people acquiring old record for religious study (8)
I believe the answer is:
theology
'religious study' is the definition.
(I've seen this before)
'those people acquiring old record' is the wordplay.
'those people' becomes 'they' (I've seen this before).
'acquiring' means one lot of letters goes inside another.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'record' becomes 'log' (logging is a kind of recording).
'o'+'log'='olog'
'they' placed around 'olog' is 'THEOLOGY'.
'for' acts as a link.
(Other definitions for theology that I've seen before include "Study of the divine" , "Study of religious questions" , "Bible study" , "Study of religious beliefs" , "Study of God, etc" .)