Bit of cloth put in river for monster (6)
I believe the answer is:
dragon
'for monster' is the definition.
(dragon is a kind of monster)
'bit of cloth put in river' is the wordplay.
'bit of cloth' becomes 'rag' (I've seen this before).
'put in' means one lot of letters goes inside another.
'river' becomes 'don' (Yorkshire river).
'rag' put into 'don' is 'DRAGON'.
(Other definitions for dragon that I've seen before include "TV investor" , "particularly intimidating woman" , "Continue interminably" , "Creature of Teutonic mythology" , "Mythical beast or lizard" .)