A driver uses a gearshift.
gearshift definition by Webster's New World
Webster's New World College Dictionary Copyright © 2010 by Wiley Publishing, Inc., Cleveland, Ohio. Used by arrangement with John Wiley & Sons, Inc.
the lever used to engage or disengage any of a number of sets of transmission gears to a motor, etc.
gearshift definition by American Heritage Dictionary
A mechanism for changing from one gear to another in a transmission.