Fig.: to treat someone influential in a servile way in order to get an advantage; to do anything possible to please someone

See how he licks his boss's boots? He's dying for a promotion!

Non vedi come lecca i piedi al capoufficio? Farebbe di tutto per una promozione!

Here's the thing: if I want to build a career here, I will have to lick the boots of my incompetent boss. I don't think it's going to happen, ever! So I'm quitting

Le cose stanno così: se voglio fare carriera qui dentro, devo leccare i piedi a quell'incompetente del mio capoufficio. Penso che non succederà mai, perciò me ne vado

In The tempest (3:2), Shakespeare used this expression in the form lick someone's shoe