Dog respectful around monsters (5)
I believe the answer is:
ogres
'monsters' is the definition.
(ogre is a type of monster)
'dog respectful around' is the wordplay.
'around' indicates a hidden word.
'OGRES' is hidden within 'dog respectful'.
(Other definitions for ogres that I've seen before include "Fairytale giants" , "Giants in fairytales" , "Gorse (anag.)" , "Formidable people" , "Awful brutes" .)