Continue to trail monster (6)
I believe the answer is:
dragon
'monster' is the definition.
(dragon is a kind of monster)
'continue to trail' is the wordplay.
'continue' becomes 'on' (I've seen this in other clues).
'to' means one lot of letters go next to another (I've seen this in other clues).
'trail' becomes 'drag' ('drag' can be a synonym of 'trail').
'on' after 'drag' is 'DRAGON'.
(Other definitions for dragon that I've seen before include "See 7" , "St George's slew one" , "particularly intimidating woman" , "kite" , "chased by addicts" .)