To apply grease to something, often as a means of lubrication. A noun or pronoun can be used between "grease" and "up." If that door creaks every time you open it, you should really grease up the hinges.
grease up
v.
To coat something completely with grease; lubricate something with grease: The mechanic greased up the motor. At the fair, they greased the pigs up and then we chased them.