grease (someone's) wheel

Translations
подмазать (кому-то) колесо
To get things done faster, you might have to grease the manager's wheel.
Чтобы дела шли быстрее, возможно, придется подмазать колесо начальника.
Definitions
To offer someone a bribe or incentive, usually in the form of money or favors, in order to encourage them to do something more quickly or easily, or to gain preferential treatment.
Words
wheel

noun
колесо
grease

verb
смазывать