Death of a Nurse by M.C. Beaton

Policeman Hamish Macbeth and his new assistant, Charlie Carter, are investigating the death of Gloria Dainty--nurse to wealthy, crotchety Mr. Harrison. Hamish had asked Gloria out on a date, but she disappeared before they could go out. Shortly after, she was found dead on the beach and it looks to Hamish like she was thrown over a cliff. Soon, he has many suspects and more deaths occur. Will Hamish again be able to solve the case, besting his superiors?