Idler is a rubbish prime minister (8)
I believe the answer is:
disraeli
'prime minister' is the definition.
(Benjamin Disraeli, Victorian prime minister)
'idler is a rubbish' is the wordplay.
'rubbish' is an anagram indicator (a poor quality or rubbish spelling of the letters).
'idler'+'is'+'a'='idlerisa'
'idlerisa' anagrammed gives 'DISRAELI'.
(Other definitions for disraeli that I've seen before include "Victorian prime minister" , "prime minister, in the past" , "C19 Prime Minister" , "I lead, sir (anag) - British PM, d. 1881" , "Ali dries out for the former British prime minister" .)