To hasten is to move or travel quickly, especially to get to a given place or to do something. You can also hasten someone to do something, meaning you pressure them to do or finish something more quickly—though this use is not as common as rush or hurry. You can also hasten an event, meaning to cause the event to happen sooner than it would have happened. For instance, the August 1991 putsch hastened the collapse of the Soviet Union means that the Soviet Union might have collapsed anyway, but it happened faster because of the August putsch.
Ex: When I learned that there was a job opening in Liverpool, I got on a train and hastened to the city to apply for it in person. I really wanted to make an impression right away.
Ex: Sarah hastened Chad to finish cooking because she was starving. She also wanted to surprise him with a trip to the theater after dinner.
To make haste is another way to say do something more quickly. Ironically, you can say make haste slowly to talk about our frustration with someone who is going to slow or to suggest that someone should work more slowly. Haste makes waste is a common phrase that means that working too quickly often results in sloppy work that will have to be redone.
Ex: Pepe looked at his watch and said that we really needed to make haste if we were going to make the show by six. We finished our coffees quickly and headed toward the movies.
Ex: I know the city has a lot of other problems, but the traffic light on our street has been broken for over a week. The councilman said they'd fix it soon, but they sure are making haste slowly! Maybe they're afraid of hurrying the job too much, as haste makes waste.