Clue: Reveal sordid business was not quite truthful — unhygienic bun riddled with penicillin (4,4,5,5,2,6)
Answer: WASH ONE’S DIRTY LINEN IN PUBLIC
Explanation: Definition: Reveal sordid business
WAS + HONES-[t]="not quite truthful" + DIRTY="unhygienic" + anagram/"riddled" of (bun + penicillin)