accelerate — If the process or rate of something accelerates or if something accelerates it, it gets faster and faster.
advance — To advance means to move forward, often in order to attack someone.
further — at or to a great distance; a long way off; at or to a remote point: We sailed far ahead of the fleet.
rush — to move, act, or progress with speed, impetuosity, or violence.
assist — If you assist someone, you help them to do a job or task by doing part of the work for them.
facilitate — to make easier or less difficult; help forward (an action, a process, etc.): Careful planning facilitates any kind of work.
hasten — to move or act with haste; proceed with haste; hurry: to hasten to a place.
promote — to help or encourage to exist or flourish; further: to promote world peace.
quicken — to make more rapid; accelerate; hasten: She quickened her pace.
speed — rapidity in moving, going, traveling, proceeding, or performing; swiftness; celerity: the speed of light; the speed of sound.
urge — to push or force along; impel with force or vigor: to urge the cause along.
dispatch — to send off or away with speed, as a messenger, telegram, body of troops, etc.
forward — toward or at a place, point, or time in advance; onward; ahead: to move forward; from this day forward; to look forward.
hurry — to move, proceed, or act with haste (often followed by up): Hurry, or we'll be late. Hurry up, it's starting to rain.
precipitate — to hasten the occurrence of; bring about prematurely, hastily, or suddenly: to precipitate an international crisis.
press — to force into service, especially naval or military service; impress.
railroad — a permanent road laid with rails, commonly in one or more pairs of continuous lines forming a track or tracks, on which locomotives and cars are run for the transportation of passengers, freight, and mail.
fast track — a racetrack dry and hard enough for optimum speed.
hand-carry — to carry or deliver by hand, as for security reasons: The ambassador hand-carried a message from the president.
hand-walk — to carry (a memorandum, check, or other document) from one person or office to another so as to assure prompt delivery.