Worthless person, erstwhile Prime Minister, shows zest (5,4)
I believe the answer is:
lemon peel
'zest' is the definition.
(I've seen this before)
'worthless person erstwhile prime minister' is the wordplay.
'worthless person' becomes 'lemon' (lemon can mean a useless person).
'erstwhile prime minister' becomes 'peel' (Robert Peel).
'lemon'+'peel'='LEMON PEEL'
'shows' is the link.
(Other definitions for lemon peel that I've seen before include "Source of zest" , "twist" .)