Clue: No-fault break-up: it might be what, say, Miley Cyrus and Liam Hemsworth had (3,4)
Answer: NUT LOAF
Explanation: Definition: it might be what, say, Miley Cyrus and Liam Hemsworth had
An anagram ('break-up') of 'no-fault'. The surface points to their divorce, but both have been vegan.