Continue slowly and tediously to find fabulous beast (6)
I believe the answer is:
dragon
I believe this is a double definition.
'continue slowly and tediously' is the first definition.
(drag on)
'fabulous beast' is the second definition.
(mythical creature)
'to find' is the link.
(Other definitions for dragon that I've seen before include "TV investor" , "St George is said to have killed one" , "particularly intimidating woman" , "Continue interminably" , "Formidable woman" .)