Subtle difference when one's leaving pest (6)
I believe the answer is:
nuance
'subtle difference' is the definition.
(I've seen this in another clue)
'one's leaving pest' is the wordplay.
'one's' becomes 'I's' (Roman numeral).
'leaving' suggests deleting specific letters.
'pest' becomes 'nuisance' (both can mean an annoying person).
'nuisance' with 'is' taken away is 'NUANCE'.
'when' is the link.
(Other definitions for nuance that I've seen before include "Fine distinction" , "Ace nun (anag)" , "Subtle distinction or variation" , "Subtle shade of difference" , "Slight difference in meaning etc" .)