Shoot nuisance besieging a city (8)
I believe the answer is:
budapest
'city' is the definition.
(Budapest is an example)
'shoot nuisance besieging a' is the wordplay.
'shoot' becomes 'bud' (I've seen this before).
'nuisance' becomes 'pest' (I've seen this before).
'besieging' indicates putting letters inside.
'bud'+'pest'='budpest'
'budpest' going around 'a' is 'BUDAPEST'.
(Other definitions for budapest that I've seen before include "city of Europe" , "Capital of Hungary" , "Hungary's capital" , "Capital city on the Danube" , "European capital" .)