It's wrong, pursuing the old monster (4)
I believe the answer is:
yeti
'monster' is the definition.
(yeti is a kind of monster)
'it's wrong pursuing the old' is the wordplay.
'wrong' is an anagram indicator.
'pursuing' says to put letters next to each other.
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'it' with letters rearranged gives 'ti'.
'ti' put after 'ye' is 'YETI'.
(Other definitions for yeti that I've seen before include "The Abominable Snowman in Tibetan" , "creature of dubious existence" , "Legendary snowman" , "Mythical humanoid" , "Mythical Himalayan beast" .)