Wiktionary
vb. (context transitive English) To consume something by first licking it from a surface.
Usage examples of "lick up".
Denninger looked and acted like the kind of man who would ride his help and bullyrag them around but lick up to his superiors like an egg-suck dog.
Then, there was a crash of falling timbers near by and Scarlett saw a thin tongue of flame lick up over the roof of the warehouse in whose sheltering shadow they sat.
Christi being ticklish squirmed deliciously, but allowed Jane to lick up as much of the excess syrup as she could.
Christi smiled gratefully, then leaned forward to lick up the spills off the floor.
The desire to lick up each shining drop nearly brought Whip to his knees.
Her tongue came out to lick up the wonderful moisture that had appeared on her lips.
And then on to the next house, while behind the flames lick up, blistering the enamels, cracking the porcelain, charring the polished wood, blackening the bright paint, smouldering the silks and rugs, crackling under the eaves.
She offered him the saucer, holding it out toward him so that all he had to do was move his head forward slightly and lick up the milk.
Watching the flames lick up, engulfing the stone as they ate away at the ancient wooden beams.