sink one's teeth into, to

Also, get one's teeth into. Become fully engaged in, as in He couldn't wait to sink his teeth into that problem. This metaphoric expression alludes to an animal biting vigorously into its prey. [Early 1900s]

To undertake an endeavor energetically: She sank her teeth into the challenging project.

To become fully engaged or engrossed in something. The analogy in this term, which began to be used figuratively only in the early twentieth century, is to the animal that bites deeply and vigorously into food. Dorothy Sayers used it in Gaudy Night (1935), describing a scholarly effort: “If one could work . . . getting one’s teeth into something dull and durable.”