Depressed politician given cold welcome (7)
I believe the answer is:
concave
'depressed' is the definition.
('concave' can be similar in meaning to 'depressed')
'politician given cold welcome' is the wordplay.
'politician' becomes 'con'.
'given' is a charade indicator (letters next to each other).
'cold' becomes 'c' (eg on taps).
'welcome' becomes 'ave' (I've seen this before).
'con'+'c'+'ave'='CONCAVE'
(Other definitions for concave that I've seen before include "Bending inwards" , "Hollowed" , "Curving inward" , "Arch" , "like a bowl" .)