No, the closest known living relatives to plesiosaurs are not sea turtles. Plesiosaurs were marine reptiles that lived during the Mesozoic era and are part of the larger group called Sauropterygia. Modern sea turtles belong to the order Testudines, which is a distinct lineage within the class Reptilia.
The closest living relatives to plesiosaurs are actually found within the group called lepidosauromorphs, which includes modern lizards and snakes, rather than marine reptiles like sea turtles. This is because both plesiosaurs and modern lepidosauromorphs share a more recent common ancestor than either does with turtles.