Death in Paradise (2011)

Scotland Yard DI Richard Poole is sent to the Caribbean island of Sainte Marie to solve a fellow policeman's murder. Having done so, he finds himself seconded to the local police force as the dead man's replacement. Poole proves to be a brilliant detective, solving several complex murders. He's not quite suited to either the pace of life on the island or the heat and sand, neither of which he likes very much. He also doesn't like seafood. That aside, the place is just great. In later series another British DI heads the investigative team, followed by an Irish DI and later again another British DI.