Refinement in pest is lacking (6)
I believe the answer is:
nuance
'refinement' is the definition.
(I know that refinement can be written as nuance)
'pest is lacking' is the wordplay.
'pest' becomes 'nuisance' (both can mean an annoying person).
'lacking' is a deletion indicator.
'nuisance' with 'is' removed is 'NUANCE'.
'in' acts as a link.
(Other definitions for nuance that I've seen before include "Subtlety of meaning" , "Subtle difference of meaning" , "Fine distinction" , "Ace nun (anag)" , "Subtle variation, in meaning say" .)