If you hasten to do something, you are quick to do it. She more than anyone had hastened to sign the contract
If you hasten to say something, you quickly add something to what you have just said in order to prevent it being misunderstood. He hastened to assure me that there was nothing traumatic to report
If you hasten an event or process, often an unpleasant one, you make it happen faster or sooner. But if he does this, he may hasten the collapse of his own country. = speed up