Next to Neil's a dog, barking (9)
I believe the answer is:
alongside
'next to' is the definition.
(I've seen this before)
'neil's a dog barking' is the wordplay.
'barking' is an anagram indicator (UK slang for mad).
'neils'+'a'+'dog'='neilsadog'
'neilsadog' anagrammed gives 'ALONGSIDE'.
(Other definitions for alongside that I've seen before include "Age-old sin (anag.)" , "Lying next to, as a boat might be" , "Side by side" , "Juxtaposed" , "Lying close to" .)