The phrase suggests an eager, proactive approach to engaging with a new endeavor or problem. After a slow start, he finally got his teeth into learning the piano.
Pro Tip 2/3
Persistence Implied
Using this phrase hints you're not just starting but also ready to persist until completion. She got her teeth into the research and wouldn't stop until every detail was perfect.
Pro Tip 3/3
Positive Connotation
It often carries a positive tone, suggesting admiration for someone's zeal or effort. He really got his teeth into organizing the charity event.