expedite
1. [ verb ] speed up the progress of; facilitate
Synonyms: hasten
Examples:

"This should expedite the process"

Related terms: help
2. [ verb ] (law) process fast and efficiently
Examples:

"I will try to expedite the matter"

Related terms: sue
Similar spelling:   expedited
  expedient
  expedition
  expediency
  expedience
  expeditious
  expediently
  except
  exhibit