Monsters turn up with Dr Seuss regularly (5)
I believe the answer is:
ogres
'monsters' is the definition.
('ogre' can be a synonym of 'monster')
'turn up with dr seuss regularly' is the wordplay.
'turn' becomes 'go' (a person's move in a board game**).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'with' means one lot of letters go next to another.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'dr'+'seuss'='drseuss'
The alternating letters of 'drseuss' are 'res'.
'go' back-to-front is 'og'.
'og'+'res'='OGRES'
(Other definitions for ogres that I've seen before include "She-giant of fairy tale" , "Terrifying types" , "Man-eating giants of folklore" , "Beasts" , "Giants in fairytales" .)