Say badger new man in Cockney house? (8)
I believe the answer is:
omnivore
'say badger' is the definition.
(I know that badger is a type of omnivore)
'new man in cockney house?' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'man' becomes 'ivor' (man's name).
'in' is an insertion indicator.
'cockney house?' becomes ''ome' ('home' - homing is a kind of housing - said with a cockney accent, dropping the 'H').
'n'+'ivor'='nivor'
'nivor' inserted inside 'ome' is 'OMNIVORE'.
(Other definitions for omnivore that I've seen before include "One who eats all kinds of foods" , "Unfussy eater" , "One's eaten everything" , "unfussy diner" , "Eater of all things" .)