Burn church after religious education investigation (8)
I believe the answer is:
research
'investigation' is the definition.
(research is investigating something)
'burn church after religious education' is the wordplay.
'burn' becomes 'sear' (sear can mean to burn).
'church' becomes 'ch' (common abbreviation).
'after' says to put letters next to each other.
'religious education' becomes 'RE' (abbreviation).
'sear'+'ch'='search'
'search' put after 're' is 'RESEARCH'.
(Other definitions for research that I've seen before include "Investigation designed to expand knowledge" , "What may make you a doctor" , "Investigate through study" , "Experimentation" , "Fact-finding" .)