Nancy's refusal to pick up rubbish (8)
I believe the answer is:
nonsense
'rubbish' is the definition.
(I've seen this before)
'nancy's refusal to pick up' is the wordplay.
'nancy's refusal' becomes 'non' ('no' in French, eg in the city of Nancy).
'to pick up' becomes 'sense' ('sense' can be a synonym of 'pick up').
'non'+'sense'='NONSENSE'
(Other definitions for nonsense that I've seen before include "Gibberish" , "Baloney" , "Rubbish; absurdity" , "'Foolishness, silliness (8)'" , "Having no intelligible meaning" .)