Asleep, a dream possesses army chaplain (5)
I believe the answer is:
padre
'army chaplain' is the definition.
(I've seen this before)
'asleep a dream possesses' is the wordplay.
'possesses' indicates the answer is hidden within the clue.
'PADRE' is hidden within 'asleep a dream'.
(Other definitions for padre that I've seen before include "Military chaplain" , "Minister" , "Army chaplain" , "Sky pilot (military slang)" , "Priest, chaplain" .)