The old twist - it is a monster (4)
I believe the answer is:
yeti
'monster' is the definition.
(yeti is a kind of monster)
'the old twist it' is the wordplay.
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'twist' is a reversal indicator (I've seen 'twisted ' mean this).
'it' written backwards gives 'ti'.
'ye'+'ti'='YETI'
'is a' is the link.
(Other definitions for yeti that I've seen before include "that you might find in mountains" , "Legendary Himalayan dweller" , "Anthropoid cryptid" , "Legendary snowman" , "Himalayan enigma" .)