Staunch supporter rightly depressed (4,4)
I believe the answer is:
true blue
'staunch supporter' is the definition.
(supporter of the Conservative Party)
'rightly depressed' is the wordplay.
'rightly' becomes 'true' (true can sometimes be an adverb).
'depressed' becomes 'blue' (I've seen this before).
'true'+'blue'='TRUE-BLUE'
(Other definitions for true blue that I've seen before include "Staunch Conservative" , "Colour of unswerving loyalty" , "Ultra-Tory" , "unlike a Tory MP at election time!" , "Completely faithful to one's principles, straight azure" .)