General:
* Rush
* Speed
* Hasten
* Expedite
* Accelerate
* Scurry
* Dash
* Hustle
*
Implying urgency:
* Haste
* Urgency
* Dispatch
* Speed up
* Step on it
Implying a less formal or more frantic pace:
* Scramble
* Rattle
* Dash
* Scamper
* Bolt
* Zoom
More specific synonyms depending on context:
* For a task: Expedite, facilitate, expedite, expedite
* For a person: Rush, scramble, dash, bolt
* For a feeling: Urgency, pressure, haste
The best synonym to use will depend on the specific context and the desired tone of your writing.