To begin doing something; to start or set about a task (intransitive).
明日から本格的に研究に取り掛かる予定だ。
I plan to get down to serious research starting tomorrow.
宿題に取り掛かる時間がない。
I don't have time to start on my homework.
早めに問題解決に取り掛かるべきだ。
You should get started on solving the problem early.