。
She immediately got to work on the new project.
Literal
She [topic-は] immediately new project [at-に] set-about.
取りかかる ('set about / get down to / start working on') is a compound: 取る ('take') + 掛かる ('hang on / engage with'). The に marks what one is setting about. Common in business and project contexts — describes the moment of transition from planning to execution. Synonyms include 始める ('start', more general) and 着手する ('commence', more formal). 企画 ('project / plan / proposal') is the standard business word for a planned undertaking.