A puzzle for theologian enveloped in anger (6)
I believe the answer is:
riddle
'a puzzle' is the definition.
(thesaurus)
'theologian enveloped in anger' is the wordplay.
'theologian' becomes 'dd' (Doctor of Divinity degree).
'enveloped in' is an insertion indicator.
'anger' becomes 'rile' (I've seen this in other clues).
'dd' going into 'rile' is 'RIDDLE'.
'for' acts as a link.
(Other definitions for riddle that I've seen before include "Run through" , "Screen" , "unsolved problem" , "Cryptic verse" , "Kind of puzzle or coarse sieve" .)