After a bit, chaps, Tango's flat (9)
I believe the answer is:
apartment
'flat' is the definition.
(I know that flat can be written as apartment)
'after a bit chaps tango's' is the wordplay.
'after' means one lot of letters go next to another.
'bit' becomes 'part' (both can mean a piece of something).
'chaps' becomes 'men' (chap can mean a man).
'tango' becomes 'T' (phonetic alphabet: alpha, bravo, charlie etc.).
'a'+'part' is 'apart'.
'apart'+'men'+'t'='APARTMENT'
(Other definitions for apartment that I've seen before include "Penthouse" , "19 across" , "property" , "Suite of rooms to live in" , "Flat (mainly US)" .)