Diana's religious followers examine entrails (7)
I believe the answer is:
dissect
'followers examine entrails' is the definition.
I can't judge whether this definition defines the answer.
'diana's religious' is the wordplay.
'diana's' becomes 'Di's' (Di is short for Diana).
'religious' becomes 'sect' (I am not sure about this - if you are sure you should believe this answer much more).
'dis'+'sect'='DISSECT'
Can you help me to learn more?
(Other definitions for dissect that I've seen before include "Analyse (something) in minute detail" , "Anatomise" , "Cut up (for study)" , "Anatomize" , "Cut open or cut apart" .)