Current despondency endless in White House (5)
I believe the answer is:
igloo
'white house' is the definition.
(I've seen this before)
'current despondency endless' is the wordplay.
'current' becomes 'I' (symbol for electric current).
'despondency' becomes 'gloom' (I've seen this before).
'endless' means to remove the last letter.
'gloom' with its last letter taken away is 'gloo'.
'i'+'gloo'='IGLOO'
'in' acts as a link.
(Other definitions for igloo that I've seen before include "Hut built of snow" , "basic dwelling" , "Inuit building" , "Snow house" , "native dwelling" .)