Police said there was "an altercation" between a motorcyclist and a car driver after the collision in North Wingfield Road, in Grassmoor, Chesterfield, at about 21:00 BST on Tuesday.
The 74 year-old man, who was driving the car, died in hospital. The biker is in police custody being questioned.
A murder investigation is under way into the death.
Det Ch Insp Gareth Meadows, who is leading the investigation, has asked anyone who witnessed the crash outside the Boot and Shoe Inn to contact the force.
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