The verb expedite means to make something happen more quickly.

Synonyms are accelerate, hasten, promote, or speed.

The word origins from Latin (1610) expeditus meaning “to remove impediments to the movement or progress of, accelerate the motion or progress of, hasten, quicken”. It is a past-participle of expediere meaning “extricate, disengage, liberate, make ready, make fit”, literally meaning “free the feet from fetters”. It is derived from ex meaning “out” plus pedis meaning “fetter, chair for the feet”.

I am willing to pay an extra fee to expedite the shipping of the package.

The client can use social media platforms to expedite the hiring process.

They are currently using the machine to expedite the production of supplies.