The insinuation is: in a pub they say you finish with nothing (8)
I believe the answer is:
innuendo
'the insinuation' is the definition.
('innuendo' can be a synonym of 'insinuation')
'a pub they say you finish with nothing' is the wordplay.
'a pub' becomes 'inn' (an inn is a type of pub).
'they say' shows a homophone (sound like).
'finish with' becomes 'end' (synonyms. I am not sure about the 'with' bit.).
'nothing' becomes 'O' (O resembles 0).
'you' sounds like 'u'.
'inn'+'u'+'end'+'o'='INNUENDO'
'is in' acts as a link.
Can you help me to learn more?
(Other definitions for innuendo that I've seen before include "Undone in unpleasant insinuation" , "Suggestiveness" , "Suggestive allusion" , "Slur" , "derogatory reference" .)