Annoying thing is involved in subtle difference (8)
I believe the answer is:
nuisance
'annoying thing' is the definition.
(I've seen this before)
'is involved in subtle difference' is the wordplay.
'involved in' indicates putting letters inside.
'subtle difference' becomes 'nuance' (I've seen this before).
'is' going inside 'nuance' is 'NUISANCE'.
(Other definitions for nuisance that I've seen before include "'Pest, annoyance (8)'" , "Trouble" , "One causing annoyance" , "Bothersome pest" , "Pest, source of annoyance" .)