Puzzle of theologian enveloped in anger (6)
I believe the answer is:
riddle
'puzzle' is the definition.
(riddling is a kind of puzzling)
'theologian enveloped in anger' is the wordplay.
'theologian' becomes 'dd' (Doctor of Divinity degree).
'enveloped in' means one lot of letters goes inside another.
'anger' becomes 'rile' (I've seen this in other clues).
'dd' put within 'rile' is 'RIDDLE'.
'of' acts as a link.
(Other definitions for riddle that I've seen before include "Perforate with gunshot - poser" , "Cryptic verse" , "Ingenious puzzle - sieve" , "It may have an answer" , "Ingenious question" .)