One logo redesigned for White House (5)
I believe the answer is:
igloo
'white house' is the definition.
(an igloo is white in colour)
'one logo redesigned' is the wordplay.
'one' becomes 'i' (Roman numeral).
'redesigned' is an anagram indicator.
'logo' with letters rearranged gives 'gloo'.
'i'+'gloo'='IGLOO'
'for' is the link.
(Other definitions for igloo that I've seen before include "Greenland dwelling" , "Ice house for Eskimo" , "Living quarters" , "basic dwelling" , "Snow-house" .)