In the late 1970s, Jacqueline Kennedy Onassis bought over 300 acres on Martha’s Vineyard and built a secluded home where she could delve into nature and books. Known as Red Gate Farm, the property came with over a mile of Atlantic Ocean beachfront near the clay cliffs of Gay Head.

Ms. Onassis’s daughter, Caroline Kennedy, is now listing the compound for $65 million. If it sells for close to its asking price, the deal would mark a record for a single-family estate on Martha’s Vineyard. The current record, $32.5 million, was…