Support company in housing American relative (6,6)
I believe the answer is:
second cousin
'relative' is the definition.
(I know that second cousin is a type of relative)
'support company in housing american' is the wordplay.
'support' becomes 'second' (eg to second an idea is to support it).
'company' becomes 'co' (abbreviation).
'housing' means one lot of letters goes inside another.
'american' becomes 'US' (United States).
'co'+'in'='coin'
'coin' enclosing 'us' is 'cousin'.
'second'+'cousin'='SECOND COUSIN'
(Other definitions for second cousin that I've seen before include "Some family" , "Relative" , "Fairly distant relation" .)