Lick and Sink Your Teeth Into

Lick

To lick something is to taste it or consume it by passing it over with your tongue, such as a lollipop or ice cream cone.
Ex: The wolves seemed to lick their lips with anticipation as they moved menacingly toward its victim.
Ex: Small children love to lick an ice cream cone on a hot summer day, but it is usually a very messy experience!
To take a licking is an expression that means to be beaten very badly or to be beaten up. If you take a licking you have not won, but have been beaten in a contest or fight.
Ex: With three of their best players injured and unable to play this Friday night, our team is getting prepared to take a licking by our long-time rivals.
Ex: Rosemary's canned goods won in all categories last year, which is why she was surprised to receive no nominations at this year's fair. She really took a licking!

Sink Your Teeth Into

To sink your teeth into means to bite vigorously or with gusto. If you sink your teeth into a certain dish, you are showing your enthusiasm for it. In a figurative sense, to sink your teeth into something means to do it with great enthusiasm, such as sinking your teeth into a new job.
Ex: If you sink your teeth into my grandmother's key lime pie, you will likely never eat a piece of store bought pie again.
Ex: After the 15-minute film on chocolate, guests at the factory are invited to the dipping room, where they can sink their teeth into chocolates from around the world.
The expression cut one's teeth on means to learn from. The job you cut your teeth on, for example, is the job where you first learned a particular skill.
Ex: The renowned tour guide loved working in Venice and other cities, but he'd cut his teeth on giving tours of his hometown, Nice, when he was just a teen.
Ex: Though the professional athlete was known for his excellent tennis skills, few people knew he had originally cut his teeth on swimming as a competitive sport.