The phrase "intrust to" is often used to indicate the act of entrusting someone with a task or responsibility. However, there are many synonyms for this phrase that can be used interchangeably depending on the context. For example, other ways to convey the same meaning include "delegate to," "assign to," or "hand over to." Similarly, you might use "charge with," "commission to," or "authorize to" depending on the nuance you want to convey. Ultimately, the choice of synonym will depend on the exact meaning and tone you want to convey when delegating responsibility.