lick at (something)
1. To lick something intensely and repeatedly. The dog just kept licking at my fingers No matter how much I lick at this suction cup, I can't get it to stick on the window.
2. Of flame, to touch or pass over something very rapidly. The flames were licking at our heels as we climbed the ladder. The fire had just begun licking at the trees when the rain began and quenched the flame.
lick at something
to draw the tongue over something repeatedly. Jimmy was just licking at the ice-cream cone, and soon it began to melt and drip off his elbow. I don't just lick at the ice cream. I take big bites of it.