How do I solve 3 down in Times Cryptic 29552?

Question

Accepted Answer

3 down reads "Cordelia Lambert’s running for MP perhaps?" (7,8 letters); the answer is LIBERAL DEMOCRAT. It's an anagram clue: the answer is a rearrangement of letters supplied by the clue itself. Look for an indicator like 'mixed', 'broken', 'cooked', or 'wild', and find a phrase whose letters add up to the answer's length. The full step-by-step breakdown is on this page.

Cordelia Lambert’s running for MP perhaps? (7,8)

3D — Cordelia Lambert’s running for MP perhaps? (7,8) — LIBERAL DEMOCRAT