Nuisance besetting European with a dated currency (6)
I believe the answer is:
peseta
'dated currency' is the definition.
(former currency of Spain)
'nuisance besetting european with a' is the wordplay.
'nuisance' becomes 'pest' (I've seen this before).
'besetting' means one lot of letters goes inside another.
'european' becomes 'E' (abbreviation e.g. EU).
'with' means one lot of letters go next to another.
'pest' going around 'e' is 'peset'.
'peset'+'a'='PESETA'
(Other definitions for peseta that I've seen before include "Spain's former currency unit" , "Old bit" , "Former Spanish currency unit" , "Old Spanish unit of money" , "Out of date bread" .)