Winged beast with rising stench, regularly in rage (7)
I believe the answer is:
griffin
'winged beast' is the definition.
'rising stench regularly in rage' is the wordplay.
'rising' shows that the letters should be reversed in order (going up in a down clue).
'stench' becomes 'niff' (niff is a kind of stench).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'in'+'rage'='inrage'
The alternating letters of 'inrage' are 'irg'.
'niff'+'irg'='niffirg'
'niffirg' written backwards gives 'GRIFFIN'.
'with' acts as a link.
(Other definitions for griffin that I've seen before include "Eagle-headed monster" , "Mythical creature" , "Mythical beast" .)