Monster depriving old horseman of oxygen (6)
I believe the answer is:
dragon
'monster' is the definition.
(I know that dragon is a type of mythical creature)
I don't understand the remainder of the clue.
(Other definitions for dragon that I've seen before include "chased by addicts" , "Intractable person" , "St George killed this flying monster" , "Fiery reptile or person" , "Fire-breathing creature slain by St George" .)