Good old King Cole - such a pest! (4)
I believe the answer is:
gnat
'a pest' is the definition.
(type of pest)
'good old king cole' is the wordplay.
'good' becomes 'g' (abbreviation).
'old king cole' becomes 'Nat' (Nat King Cole, jazz singer, 1919-1965).
'g'+'nat'='GNAT'
'such' acts as a link.
(Other definitions for gnat that I've seen before include "Any of various small biting flies" , "Something with bite" , "Woodland area" , "little irritation" , "Small, swarming insect" .)