Bother! One new conveyance outside is a nuisance (9)
I believe the answer is:
annoyance
'a nuisance' is the definition.
(synonyms)
'bother one new conveyance outside' is the wordplay.
'bother' becomes 'annoy' (synonyms).
'one' becomes 'a' (a thing is one thing).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'outside' means to remove the middle letters.
'conveyance' with its middle removed is 'ce'.
'annoy'+'a'+'n'+'ce'='ANNOYANCE'
'is' acts as a link.
(Other definitions for annoyance that I've seen before include "Feeling of slight anger" , "(Anger at) harassment" , "Nuisance" , "Pain" , "pest" .)