It happened on Cottingley Road, Allerton, around 7.45pm yesterday evening.
The Ford Focus was driving towards Cottingley and turned right at the junction with Stone Street when it collided with the grey Yamaha motorcycle, which was travelling in the opposite direction.
The motorcyclist, 30, was fatally injured.
The Ford made off and crashed into a red Volkswagen Polo. The Ford was later found abandoned on Meadow Court.
Detective Chief Inspector Mark Swift, of the Major Enquiry Team, said: “I would urgently appeal for anyone who witnessed this collision or saw the driver of the Ford make off from the scene.
“I would appeal directly to the driver of the vehicle involved to contact officers. This was a tragic incident in which a man lost his life and we want to establish the full circumstances around the collision.
“Anyone who witnessed the silver Ford Focus driving in the area prior to the collision or anyone who may have dash-cam footage of the vehicles driving in the area should get in contact with officers.”