New growth a nuisance in capital (8)

I believe the answer is:

budapest

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'capital' is the definition.
(capital of Hungary)

'new growth a nuisance' is the wordplay.
'new growth' becomes 'bud' (I can't explain this - if you can you should give a lot more credence to this answer).
'nuisance' becomes 'pest' (I've seen this before).
'bud'+'a'+'pest'='BUDAPEST'

'in' acts as a link.

Can you help me to learn more?

(Other definitions for budapest that I've seen before include "Capital city on the Danube" , "Hungary's capital" , "capital location" , "European capital" , "Capital of Hungary" .)

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