entrust
To give someone important responsibility because you trust them.
To entrust something to someone means to give them responsibility for it because you believe they'll take good care of it or handle it well. When your parents entrust you with a house key, they're showing they trust you to keep it safe and use it responsibly. When a teacher entrusts a student with feeding the class hamster over spring break, she's putting the pet's well-being in that student's hands.
The word combines trust with responsibility. You don't entrust things to just anyone: you choose someone you believe will honor that trust. A museum might entrust priceless paintings to a careful art restorer. A dying king might entrust his kingdom to his wisest advisor. A friend might entrust you with a secret, counting on you to keep it private.
Being entrusted with something is both an honor and a serious responsibility. It means someone has confidence in your character and judgment. When people entrust you with important things, whether it's watching their younger sibling, keeping a promise, or taking care of something valuable, they're saying they believe you'll do the right thing even when no one's watching.