Core supporter upset supporting Republican rubbish (7)
'rubbish' is the definition.
'core supporter upset supporting republican' is the wordplay.
'core' becomes 'hub' (**).
'supporter' becomes 'bra' (I've seen this before).
'upset' shows that the letters should be reversed in order.
'supporting' is a charade indicator (letters next to each other) (in a down clue, some letters go below others).
'republican' becomes 'r' (abbreviation).
'bra' back-to-front is 'arb'.
'hubarb' put after 'r' is 'RHUBARB'.
(Other definitions for rhubarb that I've seen before include "Reddish, fleshy-stalked plant, makes nice tart", "Plant, its stalk eaten", "Stalky fruit", "The pinkish stalks are edible, but the leaves are poisonous", "Rheum rhaponticum".)